Pre-Algebra: Polynomials Word Problems
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Pre-Algebra: Polynomials WordProblems
A box with no top is to be made from a piece of metal
A box with no top is to be made from an 8 inch by 6 inch piece of metal by cutting identical squares from each corner and turning up the sides. The volume of the box is modeled by the polynomial 4x
3-28x
2+48x. Factor the polynomial ...
Long Polynomial Division
How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school?
Suppose you are at the gas station
Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation:
C(g)=3.03(g)
a) What does the number 3.03 represent?
b) Find C(2)
c) Find C(9)
d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.
e) If you were to graph C(g), what would be an appropriate domain? ...
The mainsail of a lightning sailboat
The mainsail of a lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24 ft tall mainsail has a leech length of 26ft and if Dacron sailcloth casts $10 per square ...
A homeowner is installing a swimming pool
A homeowner is installing a swimming pool in his backyard. He wants its length to be 4 feet longer than its width. Then he wants to surround it with a concrete walkway 3 feet wide. If he can only afford 300 square feet of concrete for the ...
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 ...
A box has a volume of 1,800 cubic cm
A box has a volume of 1,800 cubic cm. The length is 6 times the height. As well, the length is 18 cm longer than the width. If the length is increased by 2 cm, the width by 3 cm and the height by 4 cm, the volume becomes 4,320 cubic ...
polynomial functions
Four boys are playing with their marbles. Two boys have the same number of marbles and they both have 1 more marble than the 3rd boy. The 4th boy has 1 marble less than the 3rd boy. If all the number of marbles of each boy is multiplied, the product would be 18...
Kattya has a square garden
Kattya has a square garden. When she increases her garden's width by 3 meters and decreases its length by 4 meters, her garden becomes 60 m
2...
Quotient
The quotient of two numbers is 4 and their difference is 39...
A company produces a product
A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit.
a) determine a function, c(x), to represent the cost production x units
b) determine a function, r(x) to represent the revenue from selling x units
c) determine a fucntion to represent profit
d) caculate break even point
Find 3 consecutive even numbers
Find 3 consecutive even numbers where the product of the smaller two numbers is 64 less than the square of the largest number.
Given a trapezoid where the small base
Given a trapezoid where the small base is 6 greater than the height and the larger base is 4 greater then three times the height, find all three dimensions (small base, large ...
A rectangular shipping container
A rectangular shipping container has a volume of 2500 cm3. The container is 4 times as wide as it is deep, and 5cm taller than it is ...
A triangle has a perimeter
A triangle has a perimeter of 197 centimeters. The sum of the smallest and medium sides is 49 cm more than the longest side. The difference of the longest side and shortest sides is 22 ...
Linda has a garden
Linda has a garden. The width of her garden is 8 feet longer than the length of it. Around the garden she has a 4 foot wide sidewalk. The area of the sidewalk is 320 feet ...
A diver stands at the very end of a diving board
A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs
2(3L-s) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long.
a) If the deflection at the end of the board is 1 ft, find c
b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6
The lenght of a rectangle
The lenght of a rectangle is 30cm less then three times the width. the perimeter of this rectangle is 180...
In a retail store, a fake diamond ring
In a retail store, a fake diamond ring cost $10 dollars. Joan buys two rings, and pays the cashier with a $2x bill. Write the expression that represents the change she would receive in polynomial form
The Robertsons put a rectangular pool
The Robertsons put a rectangular pool with a stone walkway around it in their back yard. The total length of the pool and walkway is 3 times the total width. The walkway is 2ft. wide all around.
a.) Write an expression for the area of the pool.
b.) Find the area of the pool when the total width is 10ft.
...
A catering company is designing a box
A catering company is designing a box. The volume box is to be 54 cubic inches and the bottom of the box to be a square. Suppose the bottom of the box has a width that is 3 inches smaller than the height x of the ...
A circular pond will be placed
A circular pond will be placed on a square piece of land. The length of a side of the square is 2x. The radius of the pond is x. The part of the square not covered by the pond will be planted with flowers. What is the area of the region that will be planted with ...
A photo is 4 inches longer
A photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square ...
Greenshield`s Formula can be used
Greenshield's Formula can be used to determine the amount of time a traffic light at an intersection should remain green. G = 2.1n + 3.7 G= green time in seconds n = average number of vehicles traveling in each lane per light cycle. Write a simplified expression to represent the average green light time per vehicle
Three students in an outdoor pursuits program
Three students in an outdoor pursuits program collaborated to write an adventure travel guidebook for Alberta and BC. Two local publishers are interested in marketing and publishing it and both anticipate retailing the book for $20. Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales. Publisher "B" offers an 8% royalty for any books sold up to 5000 copies and will then increase the royalty to 15% for any copies sold in excess of 5000.
a) Describe the type of function
b) Find the functions A(x) and B(x) - notice that function A(x) is apiecewise defined function.
c) Let x be the number of books sold and let A(x) give the income under plan "A" and B(x) give the income under plan "B". Graph functions on the interval 0,10000
A cuts half a rectangular lawn
A cuts half a rectangular lawn, 50 m by 20 m by mowing strips of equal width around the perimeter. B cuts the small rectangle left. How wide a strip does A cut so that A and B share the work equally??
You are designing a rectangular flower bed
You are designing a rectangular flower bed that you will border using bricks pavers. The width of the border around the bed will be the same on every side.
a. Write a polynomial that represents the total area of the flower bed and the border.
b. Find the total area of the flower bed and border when the width of the border is 1...
A manufacturer of screened porches
A manufacturer of screened porches sells a model that sells for p dollars. The revenue from the sale of this model is given by the following polynomial:
R = -0.25p
2 + 250p
If revenue is found by multiplying price by ...
A polynomial in x has degree 3
A polynomial in x has degree 3. The coefficient of x
2 is 3 less than the coefficient of x
3. Te coefficient of x is three times the coefficient of x
2. The remaining coefficient is more than the coefficient of x
3. The sum of the coefficients is -4...
A market research finds that at a price
A market research finds that at a price of p=20, they would sell x=42 tiles each month. If they up the price to p=10, then more people would purchase the tile, and they can expect to sell x=52 tiles a months ...
A square has sides of length
A square has sides of length 3x+1 meters. Find a polynomial A(x) that represents the area of the square. Find A(1)
polynomials
Superman wants to build a sidewalk around a lot. Batman says that the current width of the lot is 5 meters and the length is 7 meters. Spiderman says that the final area must be 63 square meters. And Aquaman says that the width of the walkway is X meters ...
At p dollars per ticket
Total Revenue
At p dollars per ticket, a promoter expects to sell 40,000 -1000p tickets to a concert.
a) How many tickets will she sell at $10 each?
b) At $10 per ticket, what is the total revenue?
c) Find a polynomial R(p) that represents the total revenue when tickets are p dollars each.
d) Find R(20), R(30), and R(35)
A water balloon is released from a window
A water balloon is released from a window 96 feet above the ground. The formula h=-16t
2+16t+96 describes the height of the water balloon above the ground, h, in feet, t seconds after the ...
A red ball and a green ball are simultaneously tossed
A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is ...
The volume of one of the buildings
The volume of one of the buildings in the downtown area is 839,808 cubic meters. The building is 9 times a s tall as the radio tower on top of the building. The square base has a side that is 27 times 4 meters less than the height of the radio ...
A truck and a car leave an intersection
A truck and a car leave an intersection. The truck travels south and the car travels east. When the truck had gone 24 miles, the distance between the car and the truck was four miles more than three times the distance traveled by the car heading east. Suppose the truck stops at point c and the car stops at point ...
If a vendor charges P dollars
If a vendor charges P dollars each for rugby shirts, then he expects to sell 2000-100P shirts at a tournament.
A) Find a polynomial R(P) that represents the total revenue when the shirts are P dollars.
B) Find R(5), R(10)...
From 1992 to 2003, the number of people in the United States
From 1992 to 2003, the number of people in the United States who participated in snowboarding can be modeled by
f(t) =0.013t
4-0.021t
3+0.084t
2+0.037t+1.2
where f(t) is the number of participants ( in millions) and t is the number of year since 1992...
The world`s largest swimming pool
The world's largest swimming pool is the Orthlieb Pool in Casablanca,Morocco. The length is 30 meters longer than 6 times the width. If the perimeter of the pool is 1,110 ...
Antonio is preparing to make
Antonio is preparing to make an ice sculpture. He has a block of ice that he wants to reduce in size by shaving off the same amount from the length (3ft.), width (5ft.), and height (4ft.). He wants to reduce the volume of the ice block to 24 cubic ...
You are making a srapbook
You are making a srapbook out of a picture that are 7 inches long and 5 inches wide. you want to place a border of equal width on each ...
Two rectangles have the same width
Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the ...
Two rectangles have the same width
Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 4 more square feet than the ...
If the ticket agency charges
If the ticket agency charges "p" dollars per ticket for a concert, it can sell maximum of (40000 – p) tickets. Find:
a. A polynomial to represent the total revenue with a ticket price as p dollars.
b. How many tickets will be sold for a price of $10 each.
...
The owner of a daycare center plans to have a rectangular sandbox
The owner of a daycare center plans to have a rectangular sandbox built in the outdoor play area. The width (in feet) of the sandbox is given by the polynomial 2x-5. If the length of the sandbox is designed to be 10 feet longer than the width, write a polynomial that represents the area of the sandbox.
(1) Part A: Solve the above problem using any methods, concepts, and procedures learned in this module. All work must be shown and completed in an equation editor.
(2) Part B: Write a 250 word summary of the above problem. Your written work should include but necessarily be limited to the following; an explanation of the problem, a review of the mathematical concepts involved, a critique of the method used to obtain the solution, and an interpretation of the answer. Your summary should be written in APA format, demonstrate proper use of the English ...
Polynomials
The width of a rectangle is 4 feet less than the lengh. The area is 5ft
2...
Find 3 consecutive even numbers
Find 3 consecutive even numbers where the product of the smaller two numbers is 52 less than the square of the largest number.
Consider the function
Consider the function f(x) = x
3 + 4x
2 + kx - 4
The remainder from f(x) divided by (x+2) twice the remainder from f(x) divided by (x-2)...
A ruler orders his chamberlain to collect
A ruler orders his chamberlain to collect an army from 30 houses, in such a way that he takes the same number of men from each house as he has already collected. The servant goes to the first house alone; to the second house he goes with one other and so ...
Pure acid is to be added
Pure acid is to be added to a 5% acid solution to obtain 95L of 23% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the ...
Two rectangles have same width
Two rectangles have same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 5 more square feet than the ...
Vanessa built a rectangular pen for her dogs
Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the sides of the pen. She had to buy 20 m of fencing in order to build the other sides of the ...
If a cylinder with a height of 3 inches
If a cylinder with a height of 3 inches and a raduis of 2 inches is compared to a cube with 3 inche edges which expression represents the volume of the cylinder to the volume of the cube?
Find 4 consecutive odd integers
Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
Colin has a 500 cm ribbon
Colin has a 500 cm ribbon that is cut into 3 pieces. The second piece is 3 times longer than the first. The third piece is 4 cm less than 4 times the length of the ...
Suppose the market research company find
Suppose the market research company find that at a price of p=$20, they would sell d=42 dresses each month. If the price was lower like p= $10 more people would purchase, and they expect to sell d=52 dresses in a month's time. Find the equation of the line for the demand ...
The length of a rectangle
The length of a rectangle is 5 centimeters less than twice its width the perimeter of the rectangle is 26cm what are the dimensions of the retangle?
Polynomials
Find the dimensions of a rectangle whose perimeter is 46m and whose area is 104m
2.
The width in feet of the sandbox
The width in feet of the sandbox is given by the polynomial 2x-5. If the length of the sandbox is designed to be 10 feet longer than the ...
The volume of a rectangular prism
The volume of a rectangular prism is (15r
3-17r
2-42r). If the dimensions of the prism are represented by polynomials with integral ...
The length of a rectangle
The length of a rectangle is 3 cm greater than the width. If each dimenstion is increased by 2 cm, the area is increased by 26 cm ...
The volume of a box
The volume of a box with height x, length x +1, And width 2x - 4 is given by the trinomial 2x
3 - 2 x
2 - 4 ...
The length of a rectangle
The length of a rectangle is 8 times its width. If the length was decreased by 10m and the width decreased by 2m, the area would be decreased by 162m
2...
The sides of a sandbox
The sides of a sandbox are 3x
2 and x+8 feet wide.
a. What is the area of the sandbox?
b. If the depth of the sandbox is x ...
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