6th Grade Math Inequalities Word Problems

This page is for sixth grade math students who need help, and for teachers and tutors who are looking for word problems on inequalities.

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Inequalities in sixth grade.

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Sixth Grade: Inequalities Word Problems

Victor`s goal is to earn $75 per week
Victor's goal is to earn $75 per week at his after-school job. Last month he was within $6.50 of his ...
100 fish are caught, tagged and released
100 fish are caught, tagged and released. Later, 70 fish are caught and 8 of them are ...
100 fish are caught, tagged and released
100 fish are caught, tagged and released. Later, 70 fish are caught and 8 of them are ...
solving inequalities
The sum of 2 consecutive even integers is at most 400...
Find all sets of three consecutive
Find all sets of three consecutive positive even integers whose sum is less then 30.
The post office will charge for the packages
The post office will charge for the ...
A school bus can hold 64 passengers
A school bus can hold 64 passengers. The 8 White Team has 141 ...
Absolute Value Inequalities
Your supervisor allows you to "clock-in" for your 8a.m. shift give or take 15 minutes. Let x=8 represent 8 a.m. and x=14.5 represent 2:30...
To fit correctly, the width of a machine part
To fit correctly, the width of a machine part can vary no more than 0.01 millimeter from 2.5 ...
Two people plan to share the driving
Two people plan to share the driving on a road trip. They do not want to drive any more than 9 hours but they want to travel at least 500 ...
A mixture weighing not more than 78 oz of food A
A mixture weighing not more than 78 oz of food A, and food B is to be made so that it contains at last 12 oz of nutrient per unit and the weight of 1 unit is 3 oz. in food B there is 4 oz. If there are x units of food A and y units of food B in the ...
A student scored
A student scored 71, 83, and 96 on three algebra ...
Clark is having a party at his house
Clark is having a party at his house. His father has allowed him to spend at most $20 on snack food. He'd like to buy chips that cost $4 per bag, and pretzels that cost $2 per ...
A person with no more than $25,000 to invest
A person with no more than $25,000 to invest plans to place the money in two investments. One investment is high risk, high yield; the other is low risk, low yield. At least $6000 is to be placed in the high-risk investment. Furthermore, the amount invested at low risk should be at least three times the amount invested at high risk. Find and graph a system of inequalities that describes all possibilities for placing the money in the high- and low-risk investments. Assume x to be high risk, high yield investments and y to be low ...
The Boston Celtics play
The Boston Celtics play an 82-game schedule. If they have won 41 of their first 50 ...
Students in the school band
Students in the school band are selling calendars. They earn $.40 on each calendar they sell. Their goal is to earn more than $327...
Abigail drove h hours
Abigail drove h hours at rate of 55 mi/h. She did not reach her goal of driving 385 miles for the ...
Animal feed is to be made from corn
Animal feed is to be made from corn and soybeans.  One pound of corn has 30 units of fat and 20 units of protein, and one pound of soybeans has 20 units of fat and 40 units of ...
Anne buys a plant
Anne buys a plant whose height is 6 cm.  The plant is growing at a rate of 2/3 cm per ...
Five times the difference of a number
Five times the difference of a number and 14 is at least 160...
Suppose wheat and sugar are two basic ingredients
Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker need needs 0.4 pound of wheat and 0.16 pound of sugar.

1)  Set up the inequalities representing the baker’s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar).

2)  If each loaf of bread is sold for $2.50, and each muffin is sold for $1.15...
I want to spend no less than
I want to spend no less than $6000 on a yard project and no more than $10000...
Ian wants to promote his band
Ian wants to promote his band on the internet. Site A offers website hosting for $4.95 per month with a $49.95 startup fee. Site B offers website hosting for $9.95 per month with no startup ...
You need 30 tons of rock to cover your backyard
You need 30 tons of rock to cover your backyard area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can by with a budjet for rock and trees of $2...
You have saved $52 and deposit
You have saved $52 and deposit $27 every week for 11 ...
There are 5 exams in a marking period
There are 5 exams in a marking period.  Gerry recieved grades of 70, 78, 90, and 95 on the first 4 ...
Two trucks start from the same point
Two trucks start from the same point at the same time and go in opposite directions. One truck travels at 88km/h and the other travels at 72km/...
Greg Jones is driving on a straight road
Greg Jones is driving on a straight road that passes through the town of Westview.  In Westview, there is a radio station that can be heard anywhere within a 20-mile radius of the town.  Greg started 50 miles away from Westview at noon, and he is driving at a rate of 40 miles/hour towards it.  Write an inequality, valid for the time before Greg reaches Westview, that states that his distance from ...
Assume that the mathematical model
Assume that the mathematical model C(x) = 16x + 130 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between $525,000 and $781...
The sum of Emma`s age and Julia`s age
The sum of Emma's age and Julia's age is sixty. Julia is four times older than ...
Solving Inequalities
A manufacturing company has determind that its profits P should be at least 1000000 more then 10 times the number of the manufacturing ...
The sum of two numbers
The sum of two numbers is less than 15. The second number is 3 more than the first. What are the possible values for the first of the two numbers? In your ...
Jenny wants to utilize a portion of her garden
Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the ...
You need 30 tons of rock
You need 30 tons of rock to cover the area.  If each to costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500.  Write an inequality that illustrates the problem and ...
Australian football is played on an elliptical field
Australian football is played on an elliptical field. The official rules state that the field must be between 135 and 185 meters long and between 110 and 155 meters wide.
a) Write an equation for the largest allowable playing field.
b) Write an equation for the smallest allowable playing field
c) Write an inequality that describes the possible areas of an Australian football field
Elisabeth and Madeline share a cell phone
Elisabeth and Madeline share a cell phone which their parents let them use only between 8pm and 9:30pm. Let x and y represent the number of minutes spent on the cell phone one evening by Elizabeth and Madeline respectively.

Write an inequality that models their parents' restriction on the cell phone usage.
Skate a graph of the ...
Victor`s goal is to earn
Victor's goal is to earn $75 per week.at his his after-school job. last month he was within $6.50 of his ...
You have to be 4ft. tall to ride a roller coaster
You have to be 4ft. tall to ride a roller coaster at the amusment park. Write an inequality for this ...
Jack`s systolic blood pressure
Jack's systolic blood pressure is measure to be 100 mm HG.  If the measurement error is +- 5 mm ...
What is the inequality for a graph
What is the inequality for a graph with points (0,4) and (9,0)
Solving Absolute Value Inequalities
A car rental company has two rental rates. Rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day plus $0.09 per mile. If you plan to rent for one ...
Linear Inequalities
truck A is rented for $50/day plus $.20 per mile.  truck B is rented for $20/day plus $.50 per ...
Absolute Value Inequalities
spend no less than $6000 and no more than $10,000
Absolute Value Inequalities
The organizers of a drama club wanted to sell 350 tickets to their show.  The actual sales were no more than 35 tickets from this ...
Absolute Value Inequalities
mrs. hays has promised her two teenagers tto a concert if together they save more than $25.00 of their spending money. the older teenager agrees to save twice as much as the younger ...
Absolute Value Inequalities
42% of the population supports mayor , margin of error is < 4%. actual percentage of population is p. find the equation
Absolute Value Inequalities
Katie wants to buy the newest barbie doll  set she only has $5 saved how much does katie needs to have before she can buy the barbie if it cost $24 ?
Absolute Value Inequalities
If a discount of 20%off the retail priceof a desk saves Mark $45.00...
Absolute Value Inequalities
Roschelle owns a car and a moped. she has at most 12 gal of gasoline to be used between the car and moped. the cars tank holds at most 18 gal and the moped\'s 3 gal. the mileage for the car is 20 mpg and for the moped is 100 mpg. how many gallons of gasoline should each vehicle use if roschelle wants to travel as far as ...
Absolute Value Inequalities
Roschelle owns a car and a moped. she has at most 12 gal of gasoline to be used between the car and moped. the cars tank holds at most 18 gal and the moped's 3 gal. the mileage for the car is 20 mpg and for the moped is 100 mpg. how many gallons of gasoline should each vehicle use if roschelle wants to travel as far as ...
Linear Inequalities
Suppose you are setting up a small business and have invested $16,000 to produce an item that will sell for $5.95. If each unit can be produced for $3.45...
Absolute Value Inequalities
the average numbers of cucumber in a pakage is 25. The nuber of seens in a the pakage can vary by 3. find the range of acceptable numbers of seeds in each package..
Absolute Value Inequalities
Bev was offered plan A: a flat salary of $2200 semi-monthly or plan B: $1800 semi-monthly plus a 5% commission of her sales. If Bev were confident that she could regularly bring in $9200 per month in ...
Absolute Value Inequalities
Of the 50 u.s. states 30 states border a major body of water and 14 states border a foreign country.  Seven states border both a major body of water and a foreign ...
Absolute Value Inequalities
Of the 50 u.s. states 30 states border a major body of water and 14 states border a foreign country.  Seven states border both a major body of water and a foreign ...
Solving Inequalities
You are waiting in line to buy tickets to see your favorite band. You know you will be waiting at least   80minutes. You are taking some magazines that usually take you 20 minutes a piece to ...
Solving Inequalities
there are 88 keys on a new piano. if there are 12 pianos in a room of broken pianos, some of which may have missing ...
Solving Inequalities
In a Winter Olympics 5000 -meter speed-skating events, Hans Holden scored times of 6.85, 7.04, and 6.92 minutes on his first three trials.
Use and inequality to find the times he can score on his last trial so that his average time is under 7...
Solving Inequalities
rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day plus $0.09 per mile. If you plan to rent for one ...
Linear Inequalities
the ages in years of 3 brothers are consecutive multiples of 4. three years ago the sum of their ages was less than 39...
Solving Inequalities
Jumping rope can burn 600 calories per ...
Solving Inequalities
Two integers are in the ratio 5:8. If their sum is less than 100...
Solving Inequalities
Bob has 11 more than twice as many M&M's as Tom. Brenda has 15 less than Bob. If they have 107 M&M's all ...
Solving Inequalities
Mrs. Denney is renting a car that gets 35 miles per gallon.  The rental charge is $19.50 a day plus 18 cents per mile. Her company will reimburse her for $33.00.  If Mrs. Denney rents the car for 1 ...
Linear Inequalities
Two girls agree to go on a road trip together. They travel (x + 5) miles on the first day. On the second day they travel 2 miles more than half of the distance they travelled on the first day. On the third day they drove 3 times as far as they did on the second day. If they drove 5000 miles ...
Solving Inequalities
For $16 yu can purchase a membership card which entitles you to rent movies for $2.75 each instead of $3.50 ...
Linear Inequalities
a nursery has 100 flats available for planting two exotic flowers a and b. The seed for exotic flower a costs $4 and the seed for exotic flower b costs $6 per flat. THe total cost of labor will be $20 per flat for flower a and $10 per flat for flower b. The expected income for flower a is $110 per flat and $150 per flat for flower b. If the owner of the nursery does not wish to spend more thatn $480 for seed and $1,400 for ...
Solving Inequalities
You are planning to spend no less than $6000 and no more tahn $10,000 on your landscaping ...
Solving Inequalities
Kori has at most $21 to spend at a convenience store. She buys a bag of potato chips and a soda for $2.35. If gasoline at this store costs $2.70 per gallon, how many gallons can Kori afford to buy for her ...
Solving Inequalities
Samuel begins his kindergarten year able to spell 10 words.  He is going to learn to spell 2 new words every day.  Write an inequality that can be used to determine how many days, d, it takes Samuel to be able to soell at least 75 ...
Solving Inequalities
Grace has twice as much money as Tad. Together they have $36...
Solving Inequalities
A teacher needs 2 weeks to cover each chapter in an algebra ...
Linear Inequalities
IT WILL TAKE AT LEAST 360 POINTS FOR KIKO'S TEAM TO WIN THE MATH CONTEST. THE SCORES FOR KIKO'S TEAMMATES WERE 94,82,AND 87,BUT ONE OF KIKO'S TEAMMATES LOST 2 OF THOSE POINTS FOR AN INCOMPLETE ...
Solving Inequalities
You are planning to spend at least  $6,000 and no more than $10,000 on your landscaping ...
Solving Inequalities
Jan's account balance is $3800. Of this, $750 is for rent. Jan wants to keep a balance of at leat $500. Write and solve an inequality describing how much she can withdraw & still meet these conditions
Solving Inequalities
For the hawks 80 basketball games next year you can buy seperate tickets for each game at $9 each or you could buy a season ticket for $580 at most how many games could you attend at the $9 price before spending more than the cost of the season ticket?
Solving Inequalities
A truck cna be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same ...
Solving Inequalities
kim works in the shipping department loading shipping crates with boxes. each empty crate weighs 150 ...
Solving Inequalities
a club decides to sell t-shirts for $12 as a fund-raiser. It costs $20 plus 8$ per t-shirt to make the t-...
Solving Inequalities
The average number of cucumber seeds in a package is 25. The number of seeds in the package can vary by ...
Solving Inequalities
A manufacturer produces the following two items: computer desks and bookcases. Each item requires
processing in each of two departments. Department A_has_55 hours available and department B has_39
hours available each week for production. To manufacture a computer desk requires 4 hours in
department A and 3 hours in department B while a bookcase requires 3 hours in department A and 2
hours in department B. Profits on the items are $72 and $23 respectively. If all the units can be sold,
how many of each should be made to maximize profits?

Let X be the number of computer desks that are sold and Y be number of bookcases sold.

Write down a linear inequality for the hour used in Department A
2. Write down a linear inequality for the hours used in Department B
Solving Inequalities
If you had 40 multiple choice questions and 'x' represents the number of questions answered ...
Solving Inequalities
A truck can be rented from Basic Rental for $50 per day plus $0.20 per mile. Roadrunners charges $20 per day plus $0.50 per mile to rent the same ...
Solving Inequalities
eddie plans to buy a pair of shoes and a pair of jeans. he etimates the the shoes will cost him twice as much as the pair of pants. if he wants to spend no more than $66...
Solving Inequalities
1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping ...
Solving Inequalities
A group of students agreed to rent a house for $1200 per month.  They found one more person to share the house with and rent decreased by $60 per person per ...
Solving Inequalities
A certian diet requires at least 60 units of Carbohydrates, 45 units of protein, and 30 units of fat each day. Each ounce of Supplement A provides 5 units of carbohydrates, 3 units of Protein, and 4 units of fat. Each ounce on Supplement B provides 2 units or carbohydrates, 2 units of protein, and 1 unit of fat. If supplement A costs $1.50 an ounce and Supplement B costs $1.00 per ...
Solving Inequalities
Shelly is 3 years older than michele. Four years ago the sum of their ages was 67...
Solving Inequalities
The French club is sponsoring a bake sale. If their goal is to raise at least $320, how many pastries must they sell at $2...
Solving Inequalities
The two numbers is 24.  The larger of two numbers is four less than twice the smaller.  Find the numbers
Solving Inequalities
a club decides to sell t-shirts for $12 as a fund-raiser. It costs $20 plus $8 per t-shirt to make the t-...
Solving Inequalities
If the first and third of three consecutive odd integers are added, the result is 87 less than five times the second integer. Find the third integer
Solving Inequalities
you invested a portion of $32,000 at 9% interest and the balance at 11% interest. How much did she invest at each rate if her total income from both investments was $3...
Solving Inequalities
A truck can be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same ...
Solving Inequalities
bill ate 3 apples.Amy ate 2 times as much apples. how many apples did amy eat
Solving Inequalities
Stace sells electronic supplies. Each week he earns $190 plus a commission equal to 4% of his sales. This week his goal is to earn no less than $500...
Solving Inequalities
If you had 40 multiple choice questions and \'x\' represents the number of questions answered ...
Solving Inequalities
A truck can be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same ...
Solving Inequalities
faustino sold two antiqe desks for $280 and $305 how much should he charge for the third in order to average at least $300 per desk?
Solving Inequalities
the length of a rectangle is 1 cm greater than twice the width.  If each dimension were increased by 5 cm, the area would be at least 150 cm greater.  Find the least possible dimesions
Solving Inequalities
The sum of two consecutive even integers is greater than 88...
Solving Inequalities
Clara had 22 coins, dimes and quarters. Altogether the coins are worth more than $3.40...
Inequalities
you have $50 and you are going to an amusement park. You spend $25 for the entrance  fee and $15 for food. You want to play a game that costs $.75.  Writes and solve an inequality to find the possilble numbers of times you can play the game. If you plat the game the maximum number of times, will you have spent the entire $50...
Solving Inequalities
The school system is trying to help their students be most successful. They are going to hire tutors to help. They must have more teachers than tutors. The maximum number of teachers and tutors to be hired is 50. How many tutors and how many teachers can they have?
a.write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired.
b.write an inequality that represents the statement that the maximum number of teachers and tutors is 50.

c.choose a point that satifies the ...
Inequalities
a motor boat travels 36 km downstream in 2 hours. in coming back upstream, the trip takes 3 ...
Inequalities
miss kuhl has 24 students in her class. she is going to divide them into groups of no more than 4 students. how many groups, ...
Inequalities
The sum of two positive integers is 108. One integer is three times as great as the other. Find the integers
Inequalities
Kate has $4 more than twice as much money as Joe does. Joe has $16 less than Marcia does. In all they have $220...
Inequalities
Only 5 fish can be caught in a day, how many fish can you catch in a month
Inequalities
find the greatest possible of integers such that one integer is twice the other and their sum is less than 30
Inequalities
Jumping rope can burn 600 calories per ...

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This Sixth Grade math page lists word problems on inequalities topic.