# Algebra: Equations Word Problems

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# Algebra: Equations WordProblems

Erica hiked up a mountain trial
Erica hiked up a mountain trial at 3km/h and returned at 4k/h. The entire trip took five hours 10 min including the half an hour she spent at the ...

A circle with radius 5
A circle with radius 5 has its center at (4,1). the line x-2y+4=0 intersects the circle. find the intersections

Crane A can unload the container ship
Crane A can unload the container ship in 10 hours, and crane B can unload it in 14 hours. Crane A started to unload the ship at noon and was joined by crane B at 2 P....

A bike shop rents mountain bikes
A bike shop rents mountain bikes for a $8.50 insurance charge plus $3.50 per hour. For how many hours can a person rent a bike with $32...

If a ladder is leaning against a building
If a ladder is leaning against a building, and the distance from the bottom of the ladder to the building is 8 ft. less than the length of the ladder, how high up the side of the building is the top of the ladder if the distance is 1 ...

Two satellites are orbiting earth
Two satellites are orbiting earth. The path of one has the equation x2 +y2 = 2250000. The orbit of the other is 200 km farther fro the centre of earth. In one ...

The area of a triangle
The area of a triangle is 30in

^{2}. The base of the triangle measures 2 in. more than twice the height of the ...

At the afternoon matinee movie
At the afternoon matinee movie 3 adult tickets and 4 child tickets cost $41, and 4 adult tickets and 3 child tickets cost $43...

A ball is shot into the air
A ball is shot into the air. It's height , h in metres after t seconds is modeled by h=-4.9t

^{2} + 30t +1.6...

Sarah had an idea
Sarah had an idea, what would happen if you put a golf ball inside a basketball? How much room would there be inside the basketball afterwards. Her golf ball has a radius of 1.68 inches while her basketball has a diameter of 9.4 ...

completing the square
The path of the ball for many golf shots can be modeled by a quadratic function. The path of a golf ball hit at an angle of about 10 degrees to the horizontal can be modeled by the function, h= -0.002d

^{2} + 0.4d, where h is the height of the ball, in meters, and d is the horizontal distance the ball travels, in meters, until it first hits the ground.

a) What is the maximum height reached by the ball?

b) What is the horizontal distance of the ball from the golfer when the ball reaches its maximum ...

A motor boat travels
A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of ...

Two taps turned on together
Two taps turned on together can fill a tank in 15 mins. Separately, one tap takes 16mins longer than the other tap to fill the ...

Andres and Biloy working together
Andres and Biloy, working together, can build a chicken house in 6 2/3 hours. Andres became ill after 3 hours of working with Biloy, and Biloy finished the job, continuing to work alone in 8 1/4 more ...

A town`s old street sweeper
A town's old street sweeper can clean the streets in 60 h. The old sweeper together with a new sweeper can clean the streets in 15 ...

The board of directors of a corporation
The board of directors of a corporation grant a bonus of $5000 to be divided between two employees. The senior employee receives $1200 more than the junior ...

Bob, driving a new Ford
Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving and old Chevy and traveling 10 miles per hour faster, to travel 390 ...

A software development company is getting ready
A software development company is getting ready to release a new product. The QA Director is notified the following: A Junior Verification Engineer takes 1 hour longer to fix a bug than it takes a Senior Engineer. If they can fix the bug in 5 hours working ...

A rectangular garden is 5 feet longer
A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square ...

My friends and I went to the mall
My friends and I went to the mall last Saturday. We went into Hollister. A shirt was on sale for $25.00 . 5 times the cost of the skinny jean minus the cost of the shirt equals $300.00...

A model rocket is shot into the air
A model rocket is shot into the air and its path is approximated by h = -5t

^{2} + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in ...

A rectangular lot whose perimeter
A rectangular lot whose perimeter is 360 ft. is fenced along 3 sides. An expensive fencing along the lot's length costs $20 per ft. and an inexpensive fencing along the 2 side widths costs $8 per ft. The total cost of the fencing along the 3 sides comes to $3280...

There are two phone plans
There are two phone plans. One plan has $28 one time fee, and 9 cents a min. The second is 13 cents a ...

Mark bought 114 meters of fencing
Mark bought 114 meters of fencing to enclose an area of pasture for his sheep. He plans to use all of the fencing to make a rectangle that is twice as long as it is ...

9 times the side of one square exceeds
9 times the side of one square exceeds the perimeter of the second square by 1 metre and 6 times the area of the second square exceeds 29 times the area of the first by 1 square ...

The tallest structure in the U.S.
The tallest structure in the U.S. is a TV tower in Blanchard, North Dakota. Its height is 2063 feet. A 2382-foot length of wire is to be used as a guy wire attached to the top of the ...

How do the Quarter Pounder and Whopper
How do the Quarter Pounder and Whopper with cheese measure up in the calorie department? Actually, not too well. Two Quarter Pounders and three whoppers with cheese provide 2607 calories. Even with one of each provides enough calories to bring tears to Jenny Crag's eyes-9 calories in excess of what is allowed on a 1000 calories-a-day ...

A framer at a photo gallery
A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 ...

Frank`s Specialty Coffees makes
Frank's Specialty Coffees makes a house blend from two types of coffee beans, one selling for $9.05 per pound, and the other selling for $6.25 per pound. His house blend sells for $7.37 per pound. If he is using 9lb of the 6.25/lb beans, how many pounds of the $9...

Suppose you invest $2000 today
Suppose you invest $2000 today and you don't add or subtract anything from the money to your investment for 30 yrs. If you earn 12% per year on your investment every year for 30 ...

You have made a quilt
You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet as a decorative border of uniform ...

The band boosters are organizing a trip
The band boosters are organizing a trip to a national competion for the 226-member marching band. A bus will hold 70 students and their instruments. A van will hold 8 students and their instuments. A bus costs $280 to rent for the trip. A van costs $70 to rent for the trip. The boosters have $980 to use for ...

I bought a can of varnish
I bought a can of varnish and store at temperature of 40 degree. I change to another place where the temperature was 74degree. After 2 hours the temperature of the varnish was 58 degree .If the temperature of varnish must be 68 degree for best results ...

Suppose you decide to move your garden
Suppose you decide to move your garden away from the house, so you have to use 50 feet of fencing for four sides. The length of the garden must be twice as long as the width. If the area is now 139 feet ...

A bulldozer can move 25 tons/h of material
A bulldozer can move 25 tons/h of material,and an end loader can move 18 tons/h.The bulldozer costs $75/h to operate,and the end loader costs $%0/h to operate.During a 1 hour construction company moved 204 tons at a cost of $600...

Ahmed has first half of a treasure map
Ahmed has first half of a treasure map, which indicates that the treasure is buried in the desert (2x + 6) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to the Castle Rock, walk ‘x’ paces to the North, and then walk (2x + 4) paces to the East. If they share their information, then they can find ‘x’ and save a lot of ...

It costs $5 to become a new member
It costs $5 to become a new member of a book club. There is a $10 charge per book ordered and tax is 7% on the books. Shipping and handling is free for all members. How many books were purchased by a new member if the total bill comes to $69...

The height of a batted baseball as a function of time
The height, H metres, of a batted baseball as a function of time, t seconds, since the ball was hit can be modeled by the relation H=-2.1(t-2.4)

^{2}+13.

a) what was the maximum height of the ball?

b) at what time after it was first hit did the ball reach its maximum height?

c) how far off the ground was the ball first ...

The owner of a health foods store
The owner of a health foods store determines that the demand equation for sellin a nutritional supplement is p=18 - 0.5 square root ((x-4) where p is the price of dollars and x is the number of bottles demanded per ...

A cricket jumps off the ground
A cricket jumps off the ground with an initial vertical velocity 4 feet per second.

a. Write an equation that gives the height (in feet) of the cricket as a function of the time (in seconds) since it jumps.

...

A boat traveled 126 miles
A boat traveled 126 miles downstream and back. The trip downstream took 6 hours. The trip back took 42 ...

A chemical plant is rectangular and has a length
A chemical plant is rectangular and has a length of a hundred meters and a width of sixty meters. A safety zone of uniform width surrounds the plant. if the area of the safety zone equals the area of the ...

A parallelogram has a base
A parallelogram has a base of length 2x +1 and a height of x+3 and has an area of 42 square units. Find the base and height of the parallelogram. (A=BH)

Flex drove 800 miles in x hours
Flex drove 800 miles in x hours on Monday

a) write a rational expression for his average speed.

b) On tuesday he drove for 6 hours at the same average ...

Tickets to a movie cost
Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75...

The total proceeds from a used book sale
The total proceeds from a used book sale were $115. A total of 65 books were sold. The books were priced at $1.50 and $2.00 each. How many books were sold for $1...

Rudy must play 12 commercials
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...

A community center sells
A community center sells a total of $301 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $487 in ticket ...

The side of a square house is 24 ft long
The side of a square house is 24 ft long, and the house is located on a lot which is 50 ft longer than it is wide. The perimeter of the lot is 20 ft more than 5 times the perimeter of the ...

A candy shop sells two new flavors of candy
A candy shop sells two new flavors of candy. Chewy nut and chocolate chew. Each barrel of chewy nut requires 8 pounds of nuts and 4 pounds chocolate and has a profit of $540. Each barrel of chocolate chew requires 8 pounds of nuts and 2 pounds of chocolate and has a profit of $210. There are 64 pounds of nuts and 32 pounds of chocolate in stock, and the owner does not want to buy more stock to make the ...

The length of a rectangle is 2 feet more
The length of a rectangle is 2 feet more than twice the width. The perimeter of the rectangle is 40 square feet. Find the length and width of the rectangle. (Hint: First write the length using an algebraic expression that contains width)

Two houses are for sale on the same street
Two houses are for sale on the same street. The second house has 1000 square feet less than twice the square feet of the first house. Together the houseshave 4400 square ...

Two rental airplanes were flown
Two rental airplanes were flown a total of 54 hours in one month. One plane rents for $105/h, and the other rents for $130/h. The total income from the two planes was $6570...

A total of 512 tickets were sold
A total of 512 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets ...

midpoint
If ab=6, bc=9 and ac=13, what must be true of points a,...

Tasty Bakery sells three kinds of muffins
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 25 cents each, oatmeal muffins at 30 cents each, and cranberry muffins at 35 cents each. Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins. If he spends $4.70 on 15 ...

A boy walked at the rate
A boy walked at the rate of 2mph and then rode a bicycle back the same distance at the rate of 10mph. If the entire trip took 3 ...

A grocer plans to mix candy
A grocer plans to mix candy that sells for $2 a pound with candy that sells for $4 a pound to get a mixture that sells for $2.75 a ...

A machine produces open boxes
A machine produces open boxes using square sheets of plastic. The machine cuts equal sized squares measuring 2 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up th esides. If each box must have a volume of 242 cubic inches, find the length of one side of the open ...

A mixture of 12 liters of chemical A
A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C

is required to kill a certain destructive crop insect. Commercial spray X contains 1, 2, and 2

parts, respectively, of these chemicals. Commercial spray Y contains only chemical C.

Commercial spray Z contains only chemicals A and B in equal ...

The following table gives the population
The following table gives the population (in millions) of Georgia and North Carolina in 1990 and 2003.

Year Georgia North Carolina

1990 6.5 6.8

2003 8.7 8.4

Assume that the population growths are ...

Diophantus was a famous Greek mathematician
Diophantus was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century A.D. After he died, someone described his life in this puzzle:

He was a boy for 1/6 of his life.

After 1/12 more, he acquired a beard.

After another 1/7, he married.

In the fifth year after his marriage his son was born.

The son lived half as many years as his father.

Diophantus died 4 years after his ...

Dave sold popcorn and pretzels
Dave sold popcorn and pretzels at the game. He sold a told of $336 worth of both. He sold popcorn for $2.50 and pretzels for $2 each. He sold twice as many bags of popcorn than ...

A motorcycle breaks down and the rider
A motorcycle breaks down and the rider has to walk the rest of the way to work. The motorcycle was traveling at 45 mi/hr, and the rider walks at a speed of 6 mi/hr. The distance from home to work is 25 miles, and the total time of the trip was 2 ...

Two cars started from the same point
Two cars started from the same point but traveled in opposite directions. the faster car traveled 15 kilometers faster than the slower car. after five hours the 2 cars were 575 kilometers ...

Three pumps are being used to empty a small pool
Three pumps are being used to empty a small pool. The first pump is twice as fast as the second pump. The first two pumps can empty the pool in 8 hours, while all three pumps can empty it in 6 hours. How long would it take each pump to empty the pool individually? Hint: Let x represent the fraction of the pool that the first pump can empty in one hour. Let y and z represent this fraction for the second and third ...

The population of black mountain
The population of black mountain is 40,000 and is gowing by 800 per year. The population of Hidden Valley is 67,000 and is decreasing by 550 per ...

Danny had $22.00 in loonies and toonies
Danny had $22.00 in loonies and toonies.

a) Write a linear relation for the total amount of money in terms of the number of loonies and toonies.

b) Write an equation to express the number of toonies in terms of the number of ...

A child in an airport is able to cover
A child in an airport is able to cover 291 meters in 3 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 228 meters in 4 minutes. What is the child's running speed on a still ...

At full speed, an airplane can travel
At full speed, an airplane can travel 4500 miles with the wind in 6 hours, but it requires 10 hours to travel the same distance against the wind.

what is the wind ...

systems of equations
The school that Asanji goes to is selling tickets to a play. On the first day of ticket sales the school sold 10 senior citizen tickets and 9 student tickets for a total of $200. The school took in $87 on the second day by selling 7 senior citizen tickets and 1 student ...

During a used book sale
During a used book sale, a total of 62 books were sold and $103 was made. The books were priced at $1.50 or $2.00 each. Find how many books are sold at $1.50 and how many at $2.00

A total of 50 juniors and seniors
A total of 50 juniors and seniors were to give a mathmatics test. The 35 juniors attained an average score of 80 while the 15 sneiors attained an average of 70...

copper that was 63% pure
copper that was 63% pure was melted together with copper that was 90% pure to make 18 kilograms of an alloy that was 75% ...

Find a two-digit number
Find a two-digit number where the sum of the digits is 6 and the number is 6 times the unit's digit.

Tina hiked 15km up a mountain trail
Tina hiked 15km up a mountain trail. Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/...

Tickets for a school play cost
Tickets for a school play cost $4 for adults and $2 for students. At the end of the play, the school sold a total of 105 tickets and collected $360. Write a linear system. Let x be the number of adult tickets sold and let y be the number of student tickets sold. Graph the ...

The chief executive has just requested
The chief executive has just requested that Suzie's division make 300 gallons of sparkling water to sell at $6 per gallon. She wishes to mix 3 grades of water selling for $9, $3, $4.50. She must use twice as much of the 4.50 water as the 3.00...

The sum of three numbers
The sum of three numbers is 15. The third number is nine less than the sum of the first and second number. The first number is four more than the third ...

There is a bag that contains
There is a bag that contains: blue, green, and red marbles. There is a total value of 10 marbles. There are twice as many blue marbles as there are green, and the amount of red is one more than three times the amount of ...

A piggy bank contains 20 coins
A piggy bank contains 20 coins, consisting of nickels and dimes. How many of each type of coin are there if the piggy bank contains $1...

Traci and Gene walk at the same rate
Traci and Gene walk at the same rate and jog at the same rate.Traci walks for 1 hour and jogs for 1 hour, and covers a distance of 17km. Gene walks for 2 hours and jogs for half and hour, and covers a distance of 16...

A man buys x cans of beer
A man buys x cans of beer at 30 cents each and (x+4) cans of lager at 35 cents each. The total cost is $3.35...

A supplier gives a quote for you
A supplier gives a quote for you: $3000 for 500 t-shirts; $5500 for 1000

t-shirts.

Assume there is a linear relationship between the number of t-shirts ordered (n) and the total cost (C)...

Write a mathematical expression for each number
Write a mathematical expression for each number 1 through 18, using only the number 4 and mathematical symbols. The goal is to use the fewest number of 4s as possible. No other digit can be used. NOTE: Fours can be combined to create 44, 4.4, 444, 0.4...

Rudy must play 12 commercials
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...

At the animal shelter
At the animal shelter there were 46 cats and dogs. There were 18 more dogs than ...

Quadratic Formula
To raise $1,000, the members of the Nice People Club pledged to chip in equal amounts. However, five of the Nice People did not contribute, so to make the $1,000 the rest of the members had to pay a extra $10 ...

Circle Equation
Ms.speedi is going to have jewels,which cost$100 a piece, set along the outer border of the face of her watch.the jeweler explained that she could place two jewels per cm.,but to estimate the price of the jewels,she would need to know the circumfrence of the watch.the radius of the face of the watch is 2 cm.help Ms. Speedi by finding the approximate cost of the jewels(incuding 8% tax)...

Circle Equation
The centre of the smallest circle passing through origin lies on the line X-Y+1=0 then find the coordinates of its centre.

Quadratic Formula
A rectangle is 4/3 as long as it is wide. A second rectangle is 4 meters longer and 2 meters wider than the first, and its area is twice that of the ...

Quadratic Formula
A social club charters a bus to go to Six Flags at a cost of $900. At the last minute, 5people decide not to go. This raises the cost per person by $2 each. If the cost is split evenly between all the people who go, how many people originally intended to take the ...

Two cows in four weeks can eat
Two cows in four weeks can eat all of the grass on two acres and all the grass that grows on these two acres during the four weeks. Three cows in two weeks can eat all the grass on two acres and all the grass that grows on these two acres during the two weeks. How many cows can eat in six weeks all the grass on six acres and all the grass that grows on these six acres during the six ...

Graphing Linear Equations
Mike plans on selling tickets to a play he is hosting, he will sell adult tickets for $15.00 and he will sell student tickets for $7.00. Mike would like to make $7000 on the ...

Ahmed has half of a treasure map
Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find

the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of ...

Twice the sum of a number
Twice the sum of a number and 9 is the same as 4 times the difference obtained when 6 is subtracted from the ...

Bob, traveling in a new Ford
Bob, traveling in a new Ford, travels 330 miles in the same amount of time it takes John, driving an old Chevy 10 miles per hour faster, to travel 390. How fast is Bob ...

The sum of three numbers
The sum of three numbers is 64. The second number is 3 more than the first. The third number is 11 less than twice the first. Find the numbers

The restaurant can currently seat 120 people
The restaurant can currently seat 120 people up to 4 people in each booth and up to 8 people in each table. Plan a new seating arrangement with no more than 12 sections that will hold a total of 250 people. Each section should have no more than 6 table or 6 booths and no section may have ...

Trains at each end of the 50.0-km-long Eurotunnel
Trains at each end of the 50.0-km-long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8.0 km/m faster than the train from England and they pass in 17...

there is a ring of fourteen stepping stones
there is a ring of fourteen stepping stones. A girl hops round the ring, stopping to change feet every time she has made three hops. She notices that when she has been round the ring three times, she has stopped to change feet on each one of the fourteen stones. The girl now hops round the ring, stopping to change feet every time she has made four hops. Explain ...

Coefficients
there are 150 apples and they need to split between 40 friends for 30 diffrent pies how much will each friend have in the pies

Fractional Coefficients
At a water pollution control facility one pipe can fill a tank in 4 hours. Combined with another pipe the tank can be filled in 2 hours, 24 ...

Coefficients
johnn and peter can do a piece of work in 3 3/7 days .while john works 3 days and peter works 4 days, they will finish the work .Find the time required by each to do the work

Coefficients
which equation has a graph you can trace to find the value of x that makes 8 = 2x - 6 a true statement?

i. y = 2x ii. y = -5x iii. y = 2x - 6 iv. y = -2x + 1 v. y = 7

Absolute Value Equations
Barry;s walkie talkie has a range of 2 mi. Barry is traveling on a straight highway and is at mile marker 207...

Solving Linear Equations
1. a man who is 42yrs old has a son of 12yrs old. in how many years will the father be twice as old as his son?

2. Mr. Santos, working as a salesman for a firm, gets a salary of 5000 per month plus a commission of 10% on all sales above 2000000 per month. his total gross pay last month was 21000. how much was his total sale last month?

3. Train A leaves a station 1/2 hour ahead of Train B. The trains travel on parallel tracks. Train A travels at 25km/h while train B travels at 25km/h , how many hours will it take Train B to overtake Train A?

4. Mark can finish task alone in 24days while Andrei can do the same task in 18days. If they work together, how long can they finish the task?

5. A variety of candies costing $10.50 per kg is mixed with another variety costing $15 per kg, to make a mixture of 12kg that would cost $12.50 per kg. how many kg of each variety were mixed?

6. Three hundred people attended a band concert. Reserved seat tickets were sold at $100 each while general admission tickets cost $60 each. If the sales totaled $26000, how many tickets of each type were sold?

7. Grace found some coins under her pillows. There were equal numbers of one peso coins and five peso coins. the number of twenty-five centavo coins was twice that of one peso coins. If the total value of the coins was P39 how many of each denomination did she find?

8. When Professor Recalde drives his car to school, the trip takes one hour. When he takes an FX cab, the trip takes 1 hour and 15 minutes. The speed of FX cab is 10 kilometers per hour less than Professor Recalde's speed when ...

Graphing Equations
a wedding cake measures 2 feet high in the center and the diameter of the bottom tier is 12 ...

Solving Systems of Equations using Elimination
Tickets for the school play sold at $2 each for adults and .75 cents for students. if there were four times as many adult tickets sold as student tickets, and the total receipts were $1750...

Completing The Square
i want to change the carpet in an office that measure 12 feet by 15 feet, if the carpet cost $12...

Rational Zeros
the revenue of a charter bus company depends on the number of unsold seats. If 100 seats are sold, the price is $50. Each unsold seat increases the cost per passenger by $1. Let x represent the number of unsold seats. Write and expression for the number of seats that are sold. Write and expression for the price per seat. Write and expression for the revenue. Find the number of unsold seats that will produce the maximum ...

Substitution Method
There are 3 times as many houses available with floor plan 2 than there are with floor plan 1. There are 56 houses in total that are ...

Solving Systems Of Linear Equations
Consumer Cost: a customer has $70 to spend in a grocery store. She spends %28.20 for canned goods. The remaining amount is needed to buy a total of 9 pounds of steak and chicken. If the cost per pound for steak and chicken is $6.95 and $2.80 ...

Solving Systems Of Linear Equations
In a family there are two cars. In a given week, the first car gets an average of 40 miles per gallon, and the second car gets 20 miles per gallon. The two cars combined drive a total of 1800 miles in that week, for a total gas consumption of 55 ...

Substitution Method
in the us house of representatives there are 435 members. if an appropriations bill passes the house with 85 more members voting in favor than against . how many voter in favor and how many voter against

Solving Systems Of Linear Equations
In 1920 the record for a certain race was 46.3 sec. In 1930, it was 46.2 sec. Let R(t)= the record in the race and t = the number of years since 1920.

A) find a linear function that fits the data.

B)use the function in (a) to predict the record in 2003 and in 2006.

C) find the year when the record will be 45...

Division Equations
The area of sherry's flower garden is one-fourth the area of her vegetable garden.The area of the flower garden is 17 square feet. Let X represent the area of the flower ...

Completing The Square
suppose that an open box is to be made from a square sheet of cardboard by cutting out 4-inch squares from each corner and then folding along the bottom of the ...

Solving Algebraic Equations
There were 1000 more students at the soccer game than nonstudents. Student tickets were $8.50 and nonstudent tickets were $13.25. If the total revenue for the game was $75,925...

Solving Linear Equations
In a fraction,twice the numerator is two more than the denominator.If 3 is added to the numerator and to the denominator,the new fraction is 2/3 .Find the original fraction

Completing The Square
Ball drops from 70 meter bridge. What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is ...

Systems Of Linear Equations
Michael buys two bags of chips an three boxes of pretzels for $5.13. He then buys another bag of chips and two more boxes of pretzels for $3.09...

First Degree Linear Equations
Ron and Kathy are ticket sellers for their class play. Ron sells student tickets for $2.00 each, and Kathy sells adult tickets for $4.50 each. If their total revenue for 364 tickets is $1175.50...

Substitution Method
A farmer grows only sunflowers and flax on his 240 acre farm. This year he wants to plant 80 more acres of sunflowers than ...

Solving Polynomial Equations
suppose a market research company finds that at a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile,and they can expect to sell x=52 tiles in a months time. Find the equation of the line for the demand equation. Write your answer in the form of p=mx+b

Multiplication Equations
A rectangular storage container with an open top is to have a volume of 60 cubic meters.

The length of its base is twice the width.

Material for the base costs 60 dollars per square meter.

Material for the sides costs 4 dollars per square ...

Substitution Method
a)The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.

b)The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.

c)Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.

d)What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this ...

Substitution Method
1. Bob and Sara went to a restaurant last Saturday. Sara remembers that she had a steak and Bob remembers that he had a burger. Their total bill was $22 but they don’t remember what the cost for each was. Sara remembers that her meal was twice as much as Bob’...

Division Equations
The area of sherry\'s flower garden is one-fourth the area of her vegetable garden.The area of the flower garden is 17 square feet. Let X represent the area of the flower ...

Solving Systems of Equations using Elimination
an airline baggage truck can hold 95 pieces of baggage in two seperate compartments. in one trip from the airplane to the terminal, the truck is filled to capacity. one compartment is holding 14 more than twice the other. how many pieces of baggage are in each compartment of the truck

Completing The Square
Ball drops from 70 meter bridge. What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is ...

Multi-Step Equations
A school play had a attendance of 216 people. The profit was 511.50 and they charged $3 for adults and $1.50 for ...

Solving Linear Equations
A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P ; grows as a linear function of time t, where t is the number of years after 2003.

a) How many students will be enrolled in the school in 2010...

Solving Systems Of Equations
Last month, a bookstore ran the following ad. Calculator Specials, scientific models $12 and graphing models $19 each. Sales of 5,370 were generated, with 15 more graphing ...

Completing The Square
Ahmed has the first half of a treasure map, which inducastes that the treasure is buried in the desert (2x+4) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to Castle Rock, walk 'x' paces to the North, and then walk (2x+4) paces to the East. If they share their information, then they can find 'x' and save a lot of ...

Logarithmic Equations
In 1998, the population of Country C was 26 million, and the exponential growth rate was 1% per ...

Logarithmic Equations
A kettle full of water is brought to a boil in a room with temperature 20°C. After 15 minutes the temperature of the water has decreased from 100°C to 75°...

Solving Systems Of Equations
Mack’s Tee Shirt Shack sold 36 shirts

one day. All short-sleeved tee shirts cost $12 and all

long-sleeved tee shirts cost $18. Total receipts for the

day were $522...

Solving Rational Equations
In a motorcycle race, one lap of the course is 650m. At the start of the race, Genna sets off 4 seconds after Tom does, but she drives her motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than he does.

a) Find the speed at which each of them is ...

Solving Systems Of Equations
Nancy had &18,000 in savings. She invested part of it at 7.5% interest and the rest at 9%. If the total income from the two investments was $1560...

Absolute Value Equations
A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the ...

Solving Systems Of Equations
the length of a rectangle is 5cm more than twice the width. the perimenter of the rectangle is 34 cm. find the dimensions of the rectangle

a) write an equation to model the length of the rectangle as a function of the width

b)write an equation using the fact that the perimeter of the rectangle is 34 cm

c) what are the dimentions of the rectangle

Trigonometric Equations
A pharmacist is to prepare 15 militers of special eye drops for a glaucoma patient. The eye-drop solution must have a 2% active ingredient, but the pharmamcis only has 10% solution and 1% solution in ...

Solving Quadratic Equations
family received 19 pieces of mail, consisting of magazines, bills, letters, and ads. If the received the same number of magazines as letters, three more bills than letters, and five more ads than ...

Solving Rational Equations
Jamie drove to visit her parents who live 70 miles away. On her way there, her average speed was 24 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 2 hours ...

Solving Systems Of Equations
Nancy had $18,000 in savings. She invested part of it at 7.5% interest and the rest at 9%. If the total income from the two investments was $1560...

Systems Of Equations
Caleb had 90 pencils and pens. After giving away 1/3 of his pencils and 10 pens, he had an equal number of pencils and pens ...

Solving Quadratic Equations
A number of students rented a car for $160 for a one weekend trip. if another sudent had joined the original group, each person's share of expenses would have been reduced by $8...

Rate Equation
Juan drives to work. Because of traffic problems, he averages 22 mph. He returns home averaging 32 mph. The total travel time is 2 1/4 hours. Write an expression for the time Juan takes to return ...

Solving Systems Of Equations
the sum of two integers is 64. when the smaller number is subtracted from the larger number, the difference is 26...

Solving Systems Of Equations
Two planes travel toward each other from cities that are about 450 km apart at rates of 240 km/hr and 210 km/hr. They started at the same ...

Solving Quadratic Equations
a tugboat can travel 8 mph in still water.going against a current it spends 1 hour and 20 minutes more than going the same distance of 8 miles with the ...

Midpoint
The midpoint of segment AB is (4,-3). If A is the point (-1...

Literal Equations
6c. Mark Clay has twice as many 10-centavo coins as 25-centavo coins, amounting to $6.75 in ...

Rate Equation
A repairman purchased several furnace blower motors for a total cost of $210. If his cost per motor had been $5 less, he could have purchased 1 additional ...

Solving Polynomial Equations
the polynomial 0.041h-0.018A-2.69 can be used to estimate the lung capacity,in liters,of a female with height h cm and age A years.find the lung capacity of a 50 year old woman who is 175 cm ...

Radical Equations
Use your equation from part a to approximate how many years it would take for the population to reach 7000...

Solving Systems Of Equations
A three digit number is 198 less than the number when its digits are reversed. Twice the sum of the digits is five more than seven times the tens digit. The tens digit is five less than twice the hundreds digit. Find the original number

Rate Equation
Deposit $250 in bank account that pays annual interest rate of 2%...

Differential Equations
The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 – N(t), where t is the time in years.

When t = 0, the population is 400.

When t = 3, the population is 650.

Find the population when t = 5. Round your answer to the nearest 50 mountain lions.

a. Write the implied differential equation.

b. Solve the equation to find the general solution.

c. Use the given information to find a particular solution.

...

Solving Quadratic Equations
A piece of cardboard is twice as long as it iss wide. It is to be made into a box with an open top by cutting 2-inch squares from each corner and folding up the sides. Determine a function V that represents the volume of the ...

Radical Equations
Rose cost $3.50/each; Lily Cost $2.50/each. The total of 10 flowers cost $50...

Multi-Step Equations
you and your neighbor are building fences of the same length. each piece of your fence is 60 inches long, and each piece of your neighbor's fence 45 inches long. the 60 inch fence pieces cost 30 dollar each. the 45 inch long fence pieces cost 22 dolla each. what is the shortest possible fence length that bth of you can build? how many pieces of fence do each of you need for this length of ...

Multi-Step Equations
while Michelle sat observing birds at a bird feeder, one forth of the birds flew away when they were startled by a noise.Two birds left the feeder to ggo to another stationed a few feet away. Three more birds flew into the branches of a nearbytree.Four birds remained at the ...

Polynomial Equations
The specifications for a cardboard box state that the width is 5 cm less than the length, and the height is 1 cm more than double the length. Write an equation for the volume of the box and find possible dimensions for a volume of 550 cm^3

Multi-Step Equations
The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total ticket sales were $1050...

Multi-Step Equations
Team A and team B have 20 players each.Team A has 7 girls.Team B has twice as many girls as team B has.On both teams,how many players are ...

Differential Equations
Joe is selling mix tapes for $54 each.He has a sale for 20% if you buy on Friday at no later than 12:00 noon.Martin buys 10 mix tapes at 12:00 and 3 others on Saturday.How much does the whole unit ...

Radical Equations
A repairman purchased several furnace-blower for a total cost of $210. If his cost per motor had been $5 less, he couldhave purchased 1 additional ...

Systems Of Equations
There are twice as many girls as boys on a basketball team. The girls average 18 points per game. The boys average 17 points per ...

Multi-Step Equations
Admission a baseball game is $5.00 for general admission and $7.00 for reserve seats. The receipts were $7348.00 for 1334 paid admission. How many of each ticket were ...

Quadratic Equations
Doy and his son can do a job in 4 and a half days. After they have worked for 3 days, Doy got sick, and the son finished the task in 6 more ...

Quadratic Equations
A group of office workers plans to share equally the $100 cost of giving a baby shower for a coworker. If they can get six more people to share the cost then the cost per person will decrease by $15...

Systems Of Equations
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is ...

Systems Of Equations
The drama club sold a total of 370 tickets to their spring production. Adult tickets cost $8 each and student tickets cost $5 each. If the amount sold was $2540...

Linear Equations
a group of 266 persons consists of men, women, and children. there are four times as many men as children, and twice as many woman as ...

Quadratic Equations
the product of two consecutive integers is 156 . Use the equation n(n+1)=156 to find the integers

Multi-Step Equations
THE KEYBOARD OF A PIANO HAS 7 FULL OCTAVES PLUS 2 EXTRA WHITE KEYS AND 1 EXTRA BLACK KEYS. THERE ARE 36 BLACK KEYS ON A ...

Systems Of Equations
The sum of two integers is 295,and the larger number is 40 more than 2 times the smaller ...

Linear Equations
Bob has two sacks of apples and four more apples in his pocket. Each sack contains the same number of apples. Altogether, Bob has 60 ...

Systems Of Equations
A rental car agency charges $16 per day plus 15 cents per mile to rent a certain car. Another agency charges $19 per day plus 9 cents per mile to rent the same car. How many miles will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency? (round your answer to the nearest hundredth of a ...

Systems Of Equations
Yvonne sold 15 tickets to a play. Some of the tickets were adult tickets that cost $5 each and some were children tickets that cost $2 each. All together Yvonne has $60...

Systems Of Equations
robert is twice as old as john. three years ago the sum of their ages was 27. find the age of each boy now

Multi-Step Equations
Katie has $880 in five- and twenty-dollar bills. If she has four more twenties than ...

Systems Of Equations
The total value of the quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80...

Systems Of Equations
Gonzalez Manufactoring borrowed $24000. Part of the money was borrowed at 10%, part ast 12%, and part at 14%. The annual interest was $2960, and the total amount borrowed at 10% and 12% was twice the amount borrowed at 14%...

Systems Of Equations
A total of 548 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold ...

Systems Of Equations
karlita is preparing a special dinner for her parents. she is making mango flavored catfish.she has to go to the supermarket to buy the fish and mangos. the mangos were $1.50 per pound, and the fish was $3.50 per pound. how much fish and mangos did she buy if she spent $25...

Quadratic Equations
A gardner sets 180 plants in rows. Each row contains the same number of plants. If there are 40 more plants in each row, the gardner would need 6 fewer ...

Multi-Step Equations
If A change machine contains nickels, dimes and quarters. There are 75 coins in the machine. The value of the coins is $7.25. There are five times as many nickels as ...

Algebraic Equations
the attendence at a ball game was 400 people. Student tickets cost $2 and adult tickets cost $3...

Algebraic Equations
Carol Blitz plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540...

Systems Of Equations
Mindy received 20 pear trees and 10 apple trees for $450. A week later she bought 30 pear tears and 20 apple trees for $700...

Systems Of Equations
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the

supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60

and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks

and spoons. They sold the finished products for a total of $147.20...

Systems Of Equations
there are twice as many girls in a classroom. When three new girls join the class will have 24 ...

Systems Of Equations
a vendor at a county fair wishes to invest $300 in his milkshake booth and would like his total revenue to be $900. He figures he can make a small shake for $ 0.40 anda large shake for $0.68. He plans to sell a small shake for $1.25 and a large shake for $2.00. How many of each size shake will he need to make and sell to realize his revenue

Logarithmic Equations
how many times stronger is an earthquake which measures 6 on the Richter scale than one which measures 5.5

Systems Of Equations
a two digit number is 3 times the sum of its digits. The number is also 45 less than the number formed by reversing the digits. find the number

Quadratic Equations
we have to find the maximum number of pieces for each number of certain slices

Systems Of Equations
how much of each of 30% alcohol and 80% alcohol should be added together to get 5 liters of mixture that is 50% alcohol

Systems Of Equations
mr. Towne takes loans from two banks. He borrows $300 more from the bank which charges 7% interest than from the bank which charges 8% interest. If his interest payments for one year are $126...

Differential Equations
You buy a jacket and the sales tax is 10.25% in the city of Chicago. The total cost if the jacket is $82.68. Find the initial cost of the jacket before the sales tax is applied

Systems Of Equations
Tina worked 14 hours last week and earned a total of $96 before taxes. Her job as a lifeguard pays $8 per hour, and her job as a cashier pays $6 per ...

Systems Of Equations
A group of people go to a play. Adult tickets cost $8 and tickets for the children under twelve years of age cost $5. There are 4 children under twelve. The group spends $44 for all the ...

Multi-Step Equations
three is added to a number and then the sum is multiplied by 4. the result is 16. find the number

Linear Equations
1.) In 1990, the area covered by rain forest was decreasing a about 78,000 square miles per year.Suppose that the desert areas were increasing at 50,000 square miles per year.At those rates,how many would pass before Earth's deserts cover twice the land area that the rain forests cover?

In 1990,there were about 35 million sqare miles of rain forest and 39...

Systems Of Equations
two sides of a triangle are equal. each of the two equal sides is 5 in more than the third side. the perimeter is 35 ...

Systems Of Equations
Advance tickets to a show cost $35 , and same-day tickets cost $20 . The total number of tickets sold was $50 for total receipts of $1225 ...

Systems Of Equations
A pet store recieves a shipment of pet foods at the beginning of each month. Over a three month period, the store recieved 1770 pounds of dog food, 1165 pounds of cat food, and 365 pounds of bird seed. Write and solve a system of equations to find the number of pounds of pet food in each of the three shipments. 1st shipment 60% of dog food, 25% of cat food, 15% of bird seed. 2nd shipment 50% dog food, 35% cat food, 15% bird seed. 3rd shipment 50% dog food, 45% cat ...

Systems Of Equations
Total revenues from sales of recorded R&B and pop music amounted to $8.4 billion. R&B music brought in five times as much revenue as pop ...

Systems Of Equations
If the length of a rectangular field is 24meters. This is 3meters less than twice the ...

Systems Of Equations
For their class play, Ron sold student tickets for $2.00 each and Kathy sold adult tickets for $5.50 each. If their total revenue for 29 tickets was $121.00...

Systems Of Equations
Several students decide to start a T-shirt company. After inital expenses of $280, they purchase each T-shirt wholesale for $3.99. They sell each T-shirt for $10.99...

Systems Of Equations
Talent show tickets are $3 for adults and $2 for students. Ticket sales of at least $600 are needed to cover the costs. At least 5 times as many students as adults attended. Write a system ot equations to find the number of adult and student tickets that need to be sold. Let x represent the number of adult ...

Systems Of Equations
A total of 515 tickets were sold for the school play. There were 65 more student tickets sold than adult ...

Systems Of Equations
I have a problem putting word problems into equations. Here is my word problem: At $10 per ticket, the Rhythm Kings will fill all 8000 seats in the Saint cloud Arena. For every $1 increase in ticket price, 500 tickets will go unsold. Find a linear equation that gives the number of tickets sold (n) in terms of the ticket price (p)...

Systems Of Equations
the U.S senate has 100 members. After a Certain election, there 12 more democrats than repubilcans, with no other parties ...

Systems Of Equations
pops cycle shop sells bicycles and tricycles. the number of bicycles is 1 less than 5 times the number of tricycles. all the bicycles and tricycles together have a total of 154 wheels. how many bicycles are ...

Systems Of Equations
During a football game, the parents of the football players sell pretzels and popcorn to raise money for new uniforms. They charge $3.00 for a bag of popcorn and $2.00 for a pretzel. The parents collect $112.00 in sales during the game. They sell twice as many bags of popcorn as pretzels. How many bags of popcorn do they ...

Systems Of Equations
An accountant has money in three accounts that pay 9%, 11%, and 12% in annual interest. He has twice as much invested at (% as he does at 11% and three times as much invested at 12% as he does at 11%. If the total interest from the three accounts is $520 for the year, how much is invested at each ...

Systems Of Equations
Roast beef has 25g of protein and 11g of calcium per serving. A serving of mashed potatoes has 2g of protein and 25g of ...

Systems Of Equations
Suppose that your family is going to buy a new air conditioning unit. One brand costs $1800 to buy, and $60 a month to operate. A more expensive brand costs $2600 to buy. But it is more efficient, and costs only $50 a month to ...

Systems Of Equations
A farmer raises wheat and soybeans on 215 acres. If she wants to plant 31 more acres in wheat than in ...

Systems Of Equations
suppose you invest $1500 in equipment to put pictures on T-shirts. You buy each T-shirt for $3. After you have placed the picture on a shirt you sell it for $20...

Systems Of Equations
At the book fair, hard cover books cost $7 each and paperback books cost $2 each. Dorothy spent $40 on books at the ...

Systems Of Equations
two drinks cost you $4.50. one drink was half the price of the other. find the price of each drink

Systems Of Equations
Three times a first number is 2 more than the opposite of a second number. The difference of four times the first number and the second number is 5...

Systems Of Equations
a bank teller has 73 bills in $5, $10, $20 denominations. the number of $5 bills is 1 more than 6 times the number of $10 bills. if the total value of the bills is $945...

Systems Of Equations
the length of a rectangular field is 24 meters. this is 3 meters less than twice the width. find the width

Systems Of Equations
You are making mosaic tiles from three types of stained glass. You need 6 square feet of glass for the project and you want there to be as much iridescent glass as red and blue glass combined. The cost of the sheet of glass having an area of 0.75 square foot is $6.50 for iridescent, $4.50 for red, and $5.50 for blue. How many sheets of each type should you purchase if you plan to spend $45 on the project?

Let x=number of sheets of iridescent glass; y=number of sheets of red glass; z=number of sheets of blue glass

Systems Of Equations
Will and Grace share a room. If the monthly rental is P11,50 and Will pays twice as much as ...

Systems Of Equations
The tens digit of a two digit positive number is 2 more than three times the unit's digit. If the digits are interchanged, the new number is 13 less than half the given number. Find the given integer

Algebraic Equations
a toy train has 20 cars- blue, purple and orange. there are 4 times as many blue cars as purple cars. there are 5 times as many orange cars as purple ...

Systems Of Equations
a tank was being filled with water at the rate of 1.5 gal/min. by 10 a.m., it contained 50 gal. several minutes later, the water going into the tank was turned off, the plug was pulled, and the tank drained at the rate of 2.3 gal/min. the tank was empty at 11:08 a....

Systems Of Equations
The perimeter of a triangle is 55 cm. The measure of the shortest side is 8 cm less than the middle side. The measure of the longest side is 1 cm less than the sum of the other two ...

Systems Of Equations
An investment of $110,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investment was $8280. The interest from the first investment was 2 times the interest from the ...

Systems Of Equations
the sum of two numbers is 18. If twice the smaller number is 6 more than the ...

Systems Of Equations
A total of 384 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold ...

Systems Of Equations
Billy found $3.26 in quarters and pennies. There were 12 more quarters than ...

Linear Equations
the greater of two number is 4 less than thrice the smaller nuber, and their sum is 32...

Radical Equations
Suppose that a market research company finds that at a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile, and they can expect to sell x=52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in the form p=mx+b. (hint: write an equation using two points in the form (x, p)

Linear Equations
For a certain experiment, a student requires 100 ml of a solution that is 8% HCI(hydrochloric acid). The store room has only solutions that are 5% HCI AND 15% ...

Systems Of Equations
A shipment of tv sets, some weighing 30 kg each and the others weighing 50 kg each, has a total weight of 880kg. If there are 20 tv sets all ...

Systems Of Equations
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 40 cents each, oatmeal muffins at 45 cents each, and cranberry muffins at 50 cents each. Charles buys some of each kind and chooses twice as many cranberry muffins as chocolate chip muffins. If he spends $6.45 on 14 muffins, how many chocolate chip muffins did he buy

Systems Of Equations
An individual wants to use milk and orange juice to increase the amount of calcium and vitamin A in her daily diet. An ounce of milk contains 38 milligrams of calcium and 56 micro grams of vitamin A. An ounce of orange juice contains 5 milligrams of calcium and 60 micro grams of vitamin A. How many ounces of milk and orange juice should she drink each day to provide exactly 550 milligrams of calcium and 1,200 micro grams of vitamin A

Systems Of Equations
The little town arts center charges $23 for adults, $13 for senior citizens, and %8 for children under 12 for their live performances on sunday afternoon. this past sunday, the paid revenue was $12843 for 896 tickets sold. there were 44 more children than ...

Systems Of Equations
A 10% solution of isoproply alcohol is mixed with a 20% solution of isopropyl alcohol to produce 40 liters of a 17% ...

Systems Of Equations
At the end of the year, a business has made a profit of $150,000 and is trying to calculate the amount of tax due to the federal government and to the state. The federal tax rate is 30%, and the state tax rate is 10%, but state taxes are deductible before federal taxes are calculated, and federal taxes are deductible before state taxes are calculated. In other words, state taxes are subtracted from the profits before the 30% federal tax is calculated, and federal taxes are subtracted from the profits before the 10% state tax is ...

Systems Of Equations
Mary has $5000 to invest into two accounts paying simple interest. The first accounts pays a guaranteed 8% simple interest and the second account pays a guaranteed 10% simple ...

Linear Equations
1.) In 1990, the area covered by rain forest was decreasing a about 78,000 square miles per year.Suppose that the desert areas were increasing at 50,000 square miles per year.At those rates,how many would pass before Earth\'s deserts cover twice the land area that the rain forests cover?

In 1990,there were about 35 million sqare miles of rain forest and 39...

Systems Of Equations
find the length of a rectangle with a perimeter of 114 meters if the length is 7 meters more than the width?

Radical Equations
Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: w=cr^-2 , where C is a constant, and r is the distance that the object is from the center of the ...

Systems Of Equations
A farmer has 50 animals, chickens and pigs. between the animals there are 144 legs. assuming no amputees or mutations, how many are there of each ...

Algebraic Equations
Theater sold 480 tickets. Floor seats were 30.00. Balcony seats were 24.00. total amount collected for 480 tickets was 13200...

Rate Equation
nine days ago the area covered bymold on a peice of breadwas 3 square inches.today the mold covers 9 square inches.find the rate of change in the molds area

Systems Of Equations
A total of tickets were sold for the school play. There were more student tickets sold than adult ...

Systems Of Equations
An Infinity GS35 travels at an average speed of 50 mph. The Lincoln Aviator travels at an average speed of 40 mph. In the time it takes the Lincoln to travel a certain distance, d, the Infinity travels 100 miles ...

Linear Equations
A motorboat travels 378 km in 7 hours going upstream and 258 in 3 hours going downstream. What is the speed of the boat in still ...

Quadratic Equations
a rectangular box is to be built with a 15 by 12 ft. piece of material by cutting square corners, if the volume of the box is 176 cubic ft. find the dimensions of the square corners

Systems Of Equations
Farmer John is buying cows for $10, pigs for $3, and chickens for .50 cents. He has $100 to spend and needs 100 animals. He needs at least one of each ...

Linear Equations
A person invests $36,000, partly at 5%, partly at 6%, and the remainder at 6.5%. The total annual interest is $2,190. Three times the amount invested at 6% equals the amount invested at 5% and 6.5% ...

Rate Equation
nine days ago the area covered by mold on a peice of bread was 3 square inches.today the mold covers 9 square inches.find the rate of change in the molds area

Systems Of Equations
The measure of the largest angle of a triangel is 12 less than the sum of the measures of the other two. The smallest angle measures 58 less than the ...

Systems Of Equations
A total of 816 tickets were sold for the school play. There were 66 more student tickets sold than adult ...

Systems Of Equations
the sond of two numbers is 4 more than the first. The sum of the numbers is 56. find the numbers

Line Equations
Write the equation of a line in slope intercept form: 3x+2y=6

Linear Equations
a magazine subscription service sold 6,2620 subscriptions in February and 14,211 subscriptions in June.

a. Assuming the number of subscriptions S in terms of the month M. (Hint: Let the month of January be 1. Set the rest of the month values based on the starting point.)

b. Based on your equation in part ...

Systems Of Equations
A total of 512 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold ...

Systems Of Equations
The sum of the digits of a two-digit number is 13. The number is 27

more than the number formed by interchanging the tens digit with the

ones ...

Systems Of Equations
Flying with the wind a plane went 183 km/h. Flying into the same wind plane only went 141 km/...

Systems Of Equations
A total of tickets were sold for the school play. There were more student tickets sold than adult ...

Systems Of Equations
Four oranges and five apples cost $3.56. Three oranges and four apples cost$2.76...

Linear Equations
A second tank that is curently full contains 20,000 gallons of home heating oil. This tank will be emptied through a drain pipe at the rate of twenty five gallons per minute.

How much heating oil will be in the tank after 10 minutes? One ...

Systems Of Equations
one number is 3 less than a secong number. twice the second number is 48 more than the 5 times the first. find the two numbers

First Degree Linear Equations
a number contains 2 digits. the units digits is twice than the ten's digit. if the number is inverted the new number is 39 more than the original ...

Fractional Equations
joey knows a route from 10th and maple to 29th and cedar that is 4/1/2 inches long on his map. the scale of his map is 3/4inch to one mile. which equation could be used to how many long joeys route is

Systems Of Equations
Juan goes to a bank and gets change for a

$100 bill consisting of all $10 bills, $5 bills, and $1 bills. There are

34 bills in ...

Systems Of Equations
Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister. He used twice as many 32-cent stamps as 20-cent ...

Systems Of Equations
The sum of two integers in ten. Three times the larger integer is three less than eight times the smaller ...

Systems Of Equations
The number of girls at Sky High School is 60 greater than the number of boys. If there are 1250 students all ...

Systems Of Equations
In a family there are two cars. In a given week, the first car gets an average of 20 miles per gallon, and the second car gets 25 miles per gallon. The two cars combined drive a total of 1225 miles in that week, for a total gas consumption of ...

Systems Of Equations
kristin spent $131 on shirts. fancy shirts cost $28 and plain shirts cos t$15...

Systems Of Equations
The houses on the north side of Perry Street are consecutive odd numbers. Tom and Voula are next-door neighbors and the sum of their house numbers is 524...

Systems Of Equations
the units digit of a two-digit number is one less than three times the tens digit. if the sum of the digits is 11, find the number

Systems Of Equations
the sum of the squares of two consecutive positive integers is 244. find the numbers

Systems Of Equations
A total of tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets sold ...

Quadratic Equations
THE perrimeter of a rectangle is 34cm. given that the diagonal is of length 13cm, and that the width is xcm, derive the equation x squared - 17x + 60 = 0...

Linear Equations
On a certain day two inspectors, A and B, employed by a factory, were inspecting a lot of manufactured articles. In the morning A had inspected 1500 articles before B started in. During the remainder of the morning they inspected 4000 more, A working 4 hours altogether. In the afternoon A worked 4 hours and b 2 hours, in which time they inspected 5200 ...

Systems Of Equations
The sum of the digits of a two-digit number is 4. If the order of the digits is reversed, the result is a numberthat exceeds the original number by 18...

Systems Of Equations
A shop builds chairs. Employees use two methods of building chairs. Method one takes 0.5 hours and the materials cost $6. Method two takes 1.5 hours and the materials cost $5. Next week they plan to spend 100 hours in labor and $446 hours in materials to build ...

Systems Of Equations
john pilots small planes for a living in a farming region. he earns $30 an hour for dusting crops and $45 transporting cargo. He works 40 hours a week and wants to earn $1600. How many hours should he spend on each job to earn $1600

Systems Of Equations
my son's basketball team charges adults $3.50 and children $1.50 for admission there was 220 person that attended and they made $535.50...

Systems Of Equations
Write a system of equations to solve the following problem. Let c be the number of child tickets and a be the number of adult tickets.

Each child ticket for a ride costs $2, while each adult ticket costs $6. If the ride collected a total of $148, and 38 tickets were sold, how many of each type of ticket were sold

Systems Of Equations
The length of a rectangle is 2 feet more than twice the width. The perimeter of the rectangle is 40 feet. Find the length and width of the rectangle. (Hint: First write the length using an algebraic expression that contains width. Then use the formula for the Perimeter = 2(width + length )

Systems Of Equations
Juan goes to a bank and gets change for a $50 bill consisting of all $5 bills and $1 bills. There are 22 bills in ...

Systems Of Equations
In a family there are two cars. In a given week, the first car gets an average of 40 miles per gallon, and the second car gets 35 miles per gallon. The two cars combined drive a total of 2450 miles in that week, for a total gas consumption of 65 ...

Systems Of Equations
Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21...

Systems Of Equations
a class of 195 students went on a field trip. They took 7 vehicles, some cars and some ...

Polynomial Equations
an object is dropped from a hot-air balloon 1296 feet above the ground. the height of the object is given by h=-16(t-9)(t+9)

where the height h is measured in feet, and the time t is measured in ...

Systems Of Equations
As a business owner there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company’s products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble. Model A costs $25 to make per bike where Model B costs $30 to make per bike. If your company has a total of 34 hours and $350 available per day for these two ...

Quadratic Equations
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ...

Quadratic Equations
suppose that an object is 100pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 mile from the center of the earth.)

Systems Of Equations
A total of 753 tickets were sold for the school play. There were 53 more student tickets sold than adult ...

Systems Of Equations
a certain two-digit number has a value that is 2 more than 6 times of its digits. the tens digit is 1 more than the unit digit. find the number

Systems Of Equations
galina spent $3.60 for stamps to mail packages. some were 30 cent stamps and the rest were 20 cent stamps. the number of 20 cent stamps was 2 less than the number of 30 cent ...

Systems Of Equations
Find the length and width of a rectangle lot with a perimeter of 70 meters if the length is 5 meters more than the width

Fractional Equations
BOY BOUGHT 3/8 OF HIS MONEY FOR BOOK AND 1/2 OF HIS REMAINING MONEY OF $6.25...

Quadratic Equations
A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3 km/h ...

Linear Equations
I have total of Rs 300 in coins of demonitions Re1, Rs 2, Rs 5. The no. of Rs 2 coins is 3 times the no of Rs 5 coins.Total no. is 160...

Systems Of Equations
The nickels and dimes fell on the floor. There were 12 more nickels than dimes, and the total value of the coins was $5.10...

Systems Of Equations
As a business owner there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company’s products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble. Model A costs $25 to make per bike where Model B costs $30 to make per bike. If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

* Solve the equations for the different bicycle models that can be made daily with the desired technique learned (graphing, substitution, elimination, matrix)...

Systems Of Equations
the sum of the digits of a two-digit number is 8. The value of the number is 2 less than 11 times the tens digit. Find the number

Quadratic Equations
Diagonal brace. The width of a rectangular gate is 2 meters

(m) larger than its height. The diagonal brace measures

6 ...

Polynomial Equations
Identify the polynomial written in completely factored form

8x^3 (-) 42^2 (+) 9x (+) 5

Systems Of Equations
A jar held 450 coins in nickels and quarters. Their value altogether was $62.50...

Systems Of Equations
Juan goes to a bank and gets change for a

$50 bill consisting of all $5 bills and $1 bills. There are

22 bills in ...

Systems Of Equations
The sum of two numbers is 25. If three times the smaller number is subtracted from twice the larger number, the result is 10...

Algebraic Equations
the width of a photograph is 4 cm more then three tenths of the lenth. if the width is 13 cm find the length

Quadratic Equations
the length of a rectangle is 6 inches more than it is wide. The area of the rectangle is 91 square ...

Systems Of Equations
An amount of 40% acid solution is to be mixed with enough 10% acid solution to make 25% acid solution. If there are to be 20 litres of the final ...

Systems Of Equations
supose you are staring an office cleaning service. you have spent $315 on equipment. to clean the office you use $4 worth of supplies. you charge $25...

Polynomial Equations
1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).

a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).

A company’s revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p.

b. Substitute the result you found from part a into the equation R = xp to find the revenue equation. Provide your answer in simplified form.

The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $300, and the supplier’s cost for a set of tile is $6 each. Let x represent the number of tile sets.

c. If b represents a fixed cost, what value would represent b?

d. Find the cost equation for the tile. Write your answer in the form C = mx + b.

The profit made from the sale of tiles is found by subtracting the costs from the revenue.

e. Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation.

f. What is the profit made from selling 20 tile sets per month?

g. What is the profit made from selling 25 tile sets each month?

h. What is the profit made from selling no tile sets each month? Interpret your answer.

i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.

j. How much profit would you earn from the number you found in part i?

k. What price would you sell the tile sets at to realize this profit (...

Systems Of Equations
At the latest sporting event on campus, the ticket takers counted 5,412 attendees for a total take of $18,216 in ticket sales. There were 3 children for every 2 adults and there was one senior for every 24 children. If the price per ticket is $4/Adult, $3/Child, and $2/Senior, how many adults, ...

Quadratic Equations
An open rectangular gutter is made by turning up the sides of a piece of metal 20 inches wide. The area of the cross section of the gutter is 50 inches ...

Systems Of Equations
The Madison Local High School marching band sold gift wrap to earn money for a band trip to Orlando,Florida .The gift wrap in solid colors sold for $4.00 per roll ,and the print gift wrap sold for $6.00 per roll .The total number of rolls sold was 480 ,and the total amount of money collected was $2340...

Algebraic Equations
an insurance agent receives a 12% fee on each new policy payment and a 3% fee on each renewal payment. If the agent received $1350 on total payments of $26250...

Quadratic Equations
A square mirror has sides measuring 2 feet less than the sides of a square painting. If the difference between their areas is 32 square ...

Systems Of Equations
The perimeter of a rectangle is 160ft. One fourth the length is the same as twice the width. Find the Length and the width

Systems Of Equations
The Cougars football team did a fund raisers before the season. There were twenty players on the team. Each player was responsible for selling a box of chocolate bars and a box of chocolate covered almonds. The chocolate bars sold for $2 each and the chocolate covered almonds sold for $3. The teams goal was to raise $3000...

Literal Equations
a rectangle is 1.5 times as long as it is wide. The perimeter of the rectangle is 75 inches. Find the width of the rectangle

Systems Of Equations
Juan goes to the bank to get change for $50 bill consisting of all $5 and $1 bills. There are 22 bills in ...

Rate Equations
the maximum number of units a worker can produce in a day is 30. the learning curve for the number of units N produced per day after a new employee has worked T days is N=30(1 - e^kt). after 20 days on the job, a new employee produces 12 ...

Systems Of Equations
The number of girls at Sky High School is 60 greater than the number of boys. If there are 1250 students all ...

Systems Of Equations
llida went to minewaska sate park one day this summer.all of the people at the park were either hiking or bike riding.there were 178 more hikers than bike riders.if there were a tottal of 676 people at the ...

Quadratic Equations
the sum of two numbers is 10 and the sum of their squares is 58. Find the numbers

Systems Of Equations
Big Video offers a apecial discount card that costs $9.99 for one year. With the discount card, each video rental costs $2.49. A discount card from Main Street Video costs $20.49 for one year. With the Main Street Video discount card, each video rental costs $1.79...

Systems Of Equations
The expensive ones cost $7 each, whereas the worthless ones cost $2 each. Alex spent $111 and bought three more expensive ones than worthless ...

Fractional Equations
roger has 2.30 in dimes and nickles. There are 5 more dimes than nickels, find the number of each kind of coin that he has

Algebraic Equations
The perimeter of a rectangle is 204 inches. The length exceeds the width by 42 ...

Systems Of Equations
Deanna asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 ...

Systems Of Equations
the perimeter of a rectangle is 58 cm. the width is 7 cm. less than three times the ...

Systems Of Equations
The University of Michigan's basketball team made 48 field goals in a recent game; some were 2-pointers and some were 3-...

Fractional Equations
A toy savings bank contains $17.30 consisting of nickels, dimes and quarters. Thenumber of dimes exceeds twice the number of nickels by 3, and the number of quarters is 4 less than 5 times the number of ...

Systems Of Equations
at an IMAX theater, the giant rectangular movie screen has a width 26 feet less than its length. if its perimeter is 332 ...

Solving Equations
The width of a rectangle is 15 feet less than its length, and the perimeter is 210 feet. Find the width

Solving Equations
The winner of an election for class president won by a vote of 8 to 5 with 992 ...

Systems Of Equations
Billy likes to mix two cereals for breakfast. He wants to reduce his sugar intake without giving up Sugar-O's, his favorite cereal. Sugar-O's contains 20% sugar while Health-Nut contains 5% sugar. How much of each cereal should he eat to fill a bowl with a 25g mixture which is 10% sugar

Systems Of Equations
the sum of the squares of two consecutive even intergers is 244. find the interger

Systems Of Equations
Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 kn/h while flaying back into the same wind. Find the speed of the wind and the speed of the plane in still air

Systems Of Equations
suppose that your family is going to buy a new air conditioning unit. One brand costs $1800 to buy and $60 a month to operate. A more expensive brand costs $2600 to buy,but it is more efficent, and costs $50 a month to ...

Systems Of Equations
A total of tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold ...

Systems Of Equations
Tickets for a school play cost $4 for adults and $3 dollars for children. A total of 390 tickets are sold, totalling $1380...

Systems Of Equations
At the school fair hamburgers cost $4.50 and nachos cost $3.00. If the vendor sold 37 food tickets for a total of $129...

Systems Of Equations
Three years from now a mother will be twice as old as her daughter. Seven years ago, she as three times as old as her ...

Systems Of Equations
the manager of a movie theater found that Saturday's total sales were $3675. he knew that a total of 650 tickets were sold. Adult tickets cost $7.50 and child tickets cost $4.50...

Solving Equations
Rudy must play 12 commercials during his 1-hr radio show.

Each commercial is either 30 sec or 60 sec long.

If the total commercial time during that hour is 10 ...

Algebraic Equations
Shaq shot three times as many baskets as Duane and Duane shot four more baskets than Duncan. If they shot a total of 96 ...

Solving Equations
The amount of oil used by a ship traveling at a suniform speed varies jointly with the distance and the square of the speed. If the ship uses 200 barrels of oil in traveling 500 miles at 40 miles per ...

Solving Equations
The number of computers produced by a certain factory varies jointly as the number of workers and the time they work. 400 workers can produce 120 cmputers in 2 hours, how many computers can 480 workers produce in 3 hours

Systems Of Equations
24-Karat Gold is pure gold, 12-karat gold is half gold, and 17-karat gold is an alloy that consists of 17 parts gold and 7 parts of another metal. Supoose that both pure gold and 14-karat gold are ...

Systems Of Equations
Kristen spent $131 on shirts. Fancy shirts cos $28 and plain shirts cost $15...

Systems Of Equations
Coffee worth $2.95 a pound was mixed with coffee worth $3.50 a pound to produce a blend worth $3.30 a ...

Systems Of Equations
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60

and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20...

Solving Equations
The base of a triangle exceeds the height by 4 inches. The area of the triangle is 30 square ...

Systems Of Equations
you have been put in charge of of event planning for a corporation that is having a martini cocktail hour for its guests.Your boss has given you a budget of $1000 and you would like ti order Grey Goose vodka for the VIP's and Skyy vodka for the other guests. A bottle of Grey Goose costs $30 while a bottle of Skyy costs $2. you must have 36 bottles total based on the number of guests ...

Systems Of Equations
They will be selling adult tickets for $5.00 and children's tickets for $2.00. How many tickets do they need to sell to make at least $1...

Systems Of Equations
When a plane flies into the wind, it can travel 3000 km in 6 hours. When it flies with the wind, it can travel the same distance in 5 ...

Algebraic Equations
The sum of two numbers is 35. Three times the larger number is the same as four times the smaller ...

Systems Of Equations
Museum tickets cost $5 for adults and $2 for children. one day the museum sold 1820 passes totaling $6100 in ...

Systems Of Equations
A small corporation borrowed $775,000 to expand its software line. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest was $67...

Algebraic Equations
Two tractors are removing a tree stump from the ground. The tractors are pulling at a right angle from each other with forces A and B, respectively. The resulting force, R is given by the formula: R = sqrt A^2 + B^2. Tractor A exerts a force of 300 pounds. If the resulting force is 500 ...

Algebraic Equations
candy worth $1.25 a pound were mixed with candy worth $1.50 a pound to produce a mixture worth $1.35 a ...

Systems Of Equations
Ms.Seymon invested 5400$ for one year. part at 4% and the rest at 7%. Her total interest for the year was $297...

Rational Equations
Describe two real-life examples where rational expressions are used on the job

Systems Of Equations
the sum of two numbers is 47. The sum of the larger number and twice the smaller number is 64...

Literal Equations
eight less than three times a number is 36 more than one-fourth of the number. find the number

Solving Equations
find the largest of two consecutive even integers such that three times the larger added to the small is 54.

Solving Equations
Adult tickets for a basketball game are $5 and children's $4. At the game 300 seats were filled. If the revenue from the ticket sales was $1410...

Fractional Equations
cary spent 1/3 of his class working on fraction problems and 3/6 of his class working on algebra problems. He spent the last 10 minutes of his class reading a chapter in his ...

Solving Equations
a wine maker has two large casks of wine. One wine is 8% alcohol, and the other is 18% ...

Algebraic Equations
Can you write on equation that can be used to find the temperature t based on the depth in the lake d?

Solving Equations
The length of a rectangleis 4ft longer than twice the width if the perimeter is 50ft find the length and width

Solving Equations
Mandy and Mackenzie spent the same amount of maoney at the arcade. They both played the same number of games. Mandy played $0.50 games and spend $10 on refreshments. Mackenzie played $0.75 games and spent $6 on ...

Solving Equations
The length of the top of a table is 6m greater than the width. The area is 91m ...

Solving Equations
four times the lesser of two consecutive even integers is 12 less than twice the greater ...

Fractional Equations
How much water must be evaporated from a 300 L tank of a 2% salt solution to obtain a 5% solution?

Algebraic Equations
A man bought a certain number of tin milk for 126kobo. he kept 4 tins for his own use and sold the rest at 3kobo more per tin than he pay for them, making a total profit of 14kobo on the ...

Solving Equations
Devon purchased tickets to an air show for 7 adults and 2 children. The total cost was 114 dollars. The cost of a childs ticket was 6 dollars less than the adult's ...

Solving Equations
John recently drove to visit his parents who live 840 miles away. On his way there is average speed was 24 mph faster than on his way home. If John spent a total of 24 hours ...

Literal Equations
jake ar A,and he was tolk in the town in 290 m/hr as b.find the number

Solving Equations
A rectangular room is 7 feet longer than it is wide. If the area of the room is 228 square ...

Solving Equations
a companys emplayees are working to create a new energy bar. they would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydreates and protein in the bar to supply the athlete. they want a total of 31 carbohydreates and 23 grams of protein to make the bar sufficeint. using the following table, create a system of tw equations and two unknowns to find how many tablespoons of each ingreident the bar will need. solve the sustem of equations using matirces

Line Equations
A company that manufactures bicycles has fixed cost of $300 per day and total costs of $4,300 per day for producting 100 bicycles per day. The cost C is lineraly related to production of x bicycles. Find the slope of the line joining the points associated with producting 0 and 100 ...

Solving Equations
the length of a rectangle is a 5 cm less than three times its width the perimeter is 86 cm find the length and width

Solving Equations
the width of a rectangle is 3 meters more than one-fourth its length. the perimeter is 26 ...

Solving Equations
A 240-in pipe is cut into two pieces. one piece is three times the length of the other find the length of the pieces

Solving Equations
The length of a rectangle is 4 less than twice the width. If the perimeter is 244, find the length, width

Solving Equations
Johnny buys a pair of jeans and a shirt for $60. The jeans cost three times as much as the ...

Solving Equations
A long distance phone company has a monthly fee of $7.95 and charges a rate of $0.05 per minute. Another long distance company has a monthly fee of $9.95 and charges a rate of $0.03 per ...

Solving Equations
the perimeter of a rectangle is 100. the width of the rectangle is 12less than the length. find the length and width

Literal Equations
Eight less than three times the number is 36 more than one-fourth of the number. Find the numbers

Solving Equations
A total of $560,000 is budgeted for the construction of a roadway. The pavement costs twice the amount of the base material, and the sidewalk costs one-fourth the amount of the pavement. Using these ...

Solving Equations
She can paint fence in 5 hours with tom 3 hours. How many hours for just tom

Solving Equations
You are selling tickets for a high school basketball game. Student

tickets cost $3 and general admission tickets cost $5. You sell 350

tickets and collect $1,450...

Literal Equations
Eight less than three times the number is 36 more than one-fourth of the number. Find the number

Solving Equations
the length of a rectangle is 7 feet less than one half the width. the area of the rectangle is 40 square ...

Solving Equations
the stoppint distance of d of a car after the breades are applied varies directly as the square of the speed r. If a car travelling 30 mph can stop in fo ...

Equations
A rectangular storage container with an open top is to have a volume of 70 cubic meters. The length of its base is twice the width. Material for the base costs 70 dollars per square meter. Material for the sides costs 7 dollars per square ...

Solving Equations
Your are choosing between two cell phone plans. One has a $15/mo fee and $.05/min charge. The other has a fee of $5 and charges $.07/min. At how many minutes with the two plans cost the ...

Equations
Two planes travel toward each other from cities that are 780 km apart, at rates of 190 and 200 km/h.They started at the same ...

Equations
The Coffee Shop sells a coffee blend made from two coffees, one costing $5/lb and the other costing $6/lb. If the blended coffee sells for $5.60/lb, find how much of each coffee is used to obtain the desired ...

Solving Equations
A 240 inch pipe is cut into two pieces. One piece is 3 times the length of the ...

Equations
A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the width. Material for the base costs 14 dollars per square meter. Material for the sides costs 5 dollars per square ...

Equations
Dempsey Candy company wants to make a new ...

Equations
A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 8 dollars per square meter. Find the cost of materials for the cheapest such container. A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 8 dollars per square ...

Equations
juan earns $6 per hr on Saturday and $5 per hr after school on weekends. he worked three times as many hrs on weekdays as on saturday last week and earned $105. how many hrs did he work on saturday

Equations
a piggy bank contains $6.35 in quarters and dimes. if there are 38 coins in ...

Equations
at a basketball game student tickets are sold for 4.50 each

A)write an equation that shows the income of y from the sale of x student tickets

B) How many student tickets must be sold to have 1125 in student sale tickets

Equations
You have 2 weeks to read a book for English class. The book you chose has 504 pages. You plan on reading the same amount each day. How many pages should you read each day to finish in 2 ...

Equations
82. Diagonal brace. The width of a rectangular gate is 2 meters

(m) larger than its height. The diagonal brace measures

6 ...

Equations
A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs 13 dollars per square meter. Material for the sides costs 9 dollars per square ...

Equations
the sum of three numbers is 163. The second number is twice the first, and the third is 15 more than the ...

Equations
the length of a rectange is 3 ft less than twice the width. the area of the rectange is 135ft sq. find the length oand width of the triangle

Equations
A total of 378 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets ...

Equations
To make a 10 pound mix of M&M's and peanuts worth $3.50 a ...

Equations
a picture frame measures 70 cm by 60 cm. 600 cm^2 of picture shows inside the ...

Equations
A cubic container, with sides of length, x inches, has a volume equal to x^3 cubic inches. The height of the container was decreased and the length was increased so that the volume is now modeled by the expression

x^3+4x^2-5x

By how many feet were the height and length changed?

(Hint: Volume = length times width times height)

Equations
A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 20 dollars per square meter. Material for the sides costs 4 dollars per square ...

Equations
Rudy must play 12 commercials during his 1-hour long show. Each commercial is either 30 seconds or 60 seconds long. If the total time during that hour is 10 ...

Equations
Jim needs to rent a car for a day. He has a choice of 3 different companies. American car rental charges $25 per day plus $0.35 per mile. Tommy's car rental charges $35 per day plus $0.15 per mile. Northeast car rental charges $50 per day plus $0.10 per ...

Equations
the sum of a number y an 17 is at most 36

Equations
Tickets for the play cost $4.50 for adults and $3.00 for kids. If one hundered people attended and $360 was collected from ticket ...

Equations
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...

Equations
The Riverside Dance Theater has 47 members in its dance troupe. Each member sold 75 tickets last season. Write and equation showing how many tickets each member ...

Equations
A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 11 dollars per square meter. Material for the sides costs 5 dollars per square ...

Equations
A machine cuts equal-sized squares measuring 2 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up the sides. If each box must have a volume of 242 cubic ...

Equations
Shelly has 2 times more dimes than nickels and she has $3...

Equations
A rectangular storage container with an open top is to have a volume of 30 cubic meters. The length of its base is twice the width. Material for the base costs 30 dollars per square meter. Material for the sides costs 3 dollars per square ...

Equations
The sum of 3 integers is 242. The second number is 3 more than twice the first and the the third number is 9 less than 5 times the ...

Equations
medium pizza cost $10.95 and large pizza cost $14.95. 50 pizzas sold for total $663.50...

Equations
myrtle invested 420,000 for 1 year part at 5% and part at 8%. how much was invested at 8% if the same ammount of interest was recieved from each ammount

Equations
A community center sells a total of 301 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $487 in ticket ...

Equations
Find the length of the side of a cubic boxwhose volume is 80 cubic feet.

Equations
A total of 312 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold ...

Equations
one-half of a no. decrease by one third of the no. is 9...

Equations
a famer want to bulid fece to enclose an area 8 meter long by 7 meter wide.how many meter of fencing she need

Equations
a 240-in. pipe is cut into two pieces. one piece is three times the length of the ...

Equations
A rectangle table is three times as long as it is wide. If the area is 108 ft^2, find the length and the width of the table

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A rectangular storage container with an open top is to have a volume of 30 cubic meters. The length of its base is twice the width. Material for the base costs 30 dollars per square meter. Material for the sides costs 2 dollars per square ...

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a theater sells two types of tickets to their plays. Childrens tickets and adult tickets. For todays performance they have sold total of 930 tickets. They have sold 4 times as many childrens tickets as adult ...

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a child's coin bank contains nickels, dimes, and aurters. there are three times as many nickels as dimes and there are five more quarters than nickels. the total value of the coins in the bank is $6.25...

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the sum of the squares of two consecutive even integers is 1252...

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Rudy must play 12 commercials during his 1 our radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...

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A rectangular storage container with an open top is to have a volume of 50 cubic meters. The length of its base is twice the width. Material for the base costs 50 dollars per square meter. Material for the sides costs 4 dollars per square ...

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A 50 lb. sack of bread flour will make 20 1lb. loaves of bread, and 8 pans of rolls with 120 rolls on each ...

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Investments. William opened two investment accounts for his grandson’s college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was invested at each rate?

.055x + (18,000 - x).04 = 831

.055x + 720 - .04x = 831

.015x = 111

x = 7,400

$7,400 was invested at 5.5%

$10,600 was invested at 4.0%

Radio Airplay. Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or60 sec long. If the total commercial time during thathour is 10 ...

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The perimeter of a rectangle is 202 inches. The length exceeds the width by 61 ...

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jill wants to create a rectangular garden. she purchased a box of fencing to go around her garden. each piece of fencing is 1 ft long, and the box contains a total of 24 pieces.if jill uses all of the ...

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a 36-foot pipe is divided into three pieces. One piece is twice as long as the shortest piece and the thrid piece is1 foot longer than four times the shortest piece. find the lenght of the shortest piece

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a boat travels 30 miles downstream in 15 ...

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The length of a rectangular bed is 2 feet less than 2 times its ...

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A rectangular storage container with an open top is to have a volume of 40 cubic meters. The length of its base is twice the width. Material for the base costs 40 dollars per square meter. Material for the sides costs 4 dollars per square meter. Find the cost of materials for the cheapest such conta

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A rectangular storage container with an open top is to have a volume of 50 cubic meters. The length of its base is twice the width. Material for the base costs 50 dollars per square meter. Material for the sides costs 3 dollars per square ...

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two cars travel in opposite directions, starting from th same place at the same time. one travels at an average rate of 48 miles an hour and th other averages 55 miles an ...

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use an equation to model and solve the problem- April buys eight books for $44. Paperback books cost $4 and hardback books cost $8...

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if a number multiplied by 6, and 5 is subracted from the product, the result is 19...

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a 60-foot pipe is divided into 3 pieces. One piece is twice as long as the shortest piece and the 3rd piece is 4 feet less than 5 times the shortest piece. find the length of the shortest piece

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a rectangular storage container with an open top is to have a volume of 10 m^3. The length of its baed is twice the width. material for the base costs 10 dollars per square meter. Material for the sides costs 6 dollars per square meter. Find the costs of the materials for the cheapest such container

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If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 ...

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Chelsea has to line up 48 chairs in 6 equal ...

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a total of 395 tickets were sold to the school play. there were 55 fewer tickets student tickets sold than adult tickets. How many adult tickets were sold

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Find the point on the line y = x closest to the point (3...

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Tickets to play were $4 for children and $5 for adults. if the theater sold 46 tickets for a toal of $200...

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Tony and Chelsea both worked hard over the summer. Together, they earned a total of $425. Tony earned $25 more than Chelsea did. How much did each of them ...

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a plot of ground is to be enclosded by a rectangular fence. fencing for three sides costs 8 per foot. Fencing for the fourth side costs 24 per foot. use the techniques of calculus to find the maximum area that can be enclosed for $8000

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if one half of a number is 5 less than one- third of the number, find the number

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The sum of two numbers is 360. Their difference is 30...

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Frank’s Specialty Coffees makes a house blend from two types of coffee

beans, one selling for $9.05 per pound, and the other selling for $6.25 per

pound. His house blend sells for $7.37 per pound. If he is using 9 lb of

the $6.25/lb beans, how many pounds of the $9.05/lb beans does he need

to make his house blend

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The cost of 150 brochures is $29 and the ost of 200 brochures is $35...

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In a basketball game, Will scored 26 points, consisting only of three-point shots and two-point shots. He made a total of 11 ...

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A total of tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold . How many adult tickets were sold

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A 90-meter path surrounds a rectangular garden. The width of the garden is two-thirds its ...

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you need to put a fence around a rectangular garden that has a perimeter of 64 feet. The width is 12 feet less than the length. Find the length and width of the garden using an equation

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A certain molecule contains twice as many atoms of hydrogen as oxygen and one more atom of carbon than hydrogen. If there are 21 atoms altogether in the ...

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the sum of two consecutive check numbers is 357. Find the numbers

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P=15+1/2D now find the depth of a diver when the pressure on the diver is 45 pounds per square inch.

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130 individual slippers were made. Twice as many slippers were made for bats than ...

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A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 3 dollars per square ...

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A rectangular storage container with an open top is to have a volume of 60 cubic meters. The length of its base is twice the width. Material for the base costs 60 dollars per square meter. Material for the sides costs 8 dollars per square ...

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The perimeter of a rectangle is 88 inches. The length exceeds the width by 14 ...

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The machine cuts equal-sized squares measuring 2 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up the sides. If each box must have a volume of 242 cubic ...

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A 60 foot pipe is divided into 3 pieces. one piece is twice as long as the shortest piece and the 3rd piece is 4 feet less than 5 times the shortest ...

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The coin container on a bus has 10 more nickels than dimes and together the nickels and dimes are worth $3.50...

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5 times the sum of 3 consecutive numbers is 1185. Find the 3 numbers

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(1 pt) A rectangular storage container with an open top is to have a volume of 80 cubic meters. The length of its base is twice the width. Material for the base costs 80 dollars per square meter. Material for the sides costs 8 dollars per square ...

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the manager of farmers delight bought a load of watermelons for $750 and priced the watermelons so that he would make $2 on each melon. when all but 100 of the melons had been sold, he broke ...

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the width of a rectangular room is 4/7 of its length, x,and its perimeter is ...

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While on a four-week hiking trip in the

mountains, the Tryon family washed 11 loads of clothes

at The Mountain View Laundry. The 20-lb capacity

washing machine costs $1.50 per load while the 30-lb

costs $2.50. Their total laundry expense was $20.50...

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A company has determined that the profit, in dolalrs, it can expect form the manufacture and sale of x tennis racquets is given by P=-0.01x^2+168x-120 How many racquets should the company manufacture and sell to earn a profit of $518...

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A collection of 64 c coins containing only nickels and dimes is worth $4.50...

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Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total of commercial time during that hour is 10 ...

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There were a total of 575 people that bought either popcorn or a candy bar at the Charolotte Eagle's men's soccer game. Each person bought only one item. The price of each bag of popcorn wa $2.50 and each candy bar was $2.00. The popcorn and candy bar sales brought in $1,275. How many bags of ...

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A rectangular storage container with an open top is to have a volume of 30 cubic meters. The length of its base is twice the width. Material for the base costs 30 dollars per square meter. Material for the sides costs 8 dollars per square ...

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Shelly is 5 years older than Michele. Four years ago the sum of their ages was 63...

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The area of jenny’s garden is one-twelfth the area of her entire yard. The area of the garden is 10 square ...

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ma hs 150 coins,all nickels and dimes. he has 12 more dimes than ...

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A total of 228 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold . How many adult tickets were sold

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You have one board that measures 3 feet and 7 inches. Another board measures 4 ...

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Shoes cost $20 a pair and boots cost $60 dollars a pair. Arlene and Jerry spent $8000 and bought 3 times as many boots as ...

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A 36 foot pipe is divided into three pieces. One piece is twice as long as the shortest piece, and the third piece is 1 foot longer than four times the shortest piece. find the length of the shortest piece

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The perimeter of a rectangle is 250 inches. The length exceeds the width by 57 inches. Find the length and the width

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A group of friends decides to buy a vacation house for $210,000, sharing the cost equally. One of the friends has to drop out of the deal. This raises the price for htose remaining in the group by $5000 a ...

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The lowest point on the African continent is the Qattarah Depression in the Sahara Desert, 436 feet below sea level. The lowest point on the North American continent is Death Valley, California, 282 feet below sea ...

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the perimeter of a rectangle is 242. the length exceeds the width by 45 inches . find the length and width

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There were a total of 575 people that bought either popcorn or a candy bar at the Charolotte Eagle\'s men\'s soccer game. Each person bought only one item. The price of each bag of popcorn wa $2.50 and each candy bar was $2.00. The popcorn and candy bar sales brought in $1,275. How many bags of ...

Equations
A rectangular storage container with an open top is to have a volume of 14 cubic meters. The length of its base is twice the width. Material for the base costs 11 dollars per square meter. Material for the sides costs 9 dollars per square ...

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The length of a rectangle is twice the width. the area 242 yd^2. find the length and the width

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Jake is now one-quarter of his father's age and in 7 years his age will be one-third the age of his father

How many years old is Jake now?

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