One Variable Inequalities Word Problems

Gabriel must practice piano at least 15 hours a week.  This week, he has practiced 6 hours so far.  Piano lessons are part of Gabriel’s practice time. Each lesson is 2 hours long. Which inequality can be used to find x, the minimum number of lessons Gabriel must attend this week?

• x + 6 ≤ 15

• 
  2x + 6 ≤ 15

• x + 6 ≥ 15

• 2x + 6 ≥ 15

Tags

7.10.A

Nathaniel runs in a charity race where $2.50 is donated for each kilometer he runs. Each runner of the race starts with a $10 donation regardless of the number of kilometers run. Nathaniel wishes to run enough kilometers to donate a minimum of $40 to charity. Write an inequality that Nathaniel can use to find the minimum number of kilometers that he must run so that he can donate a minimum of $40 to charity.

• 2.50x + 10 ≥ 40

• 2.50x + 10 ≤ 40

• 10x + 2.50 ≤ 40

• 10x + 2.50 ≤ 40

Tags

7.10.A

The greatest weight a moving truck can carry is 1,600 pounds. The truck is loaded with a piano that weighs 400 pounds. Boxes that weigh 50 pounds each will also be loaded into the truck.

Write an inequality that represents all possible values of x, the number of these boxes that can be loaded into the moving truck.

• 50x + 400 ≤ 1600

• 50x + 400 ≥ 1600

• 400x + 50 ≥ 1600

• 50x - 400 ≥ 1600

Tags

7.10.A

A principal has given a class $75 to help pay for a field trip to a zoo. The students in the class are selling pies for $5 each to earn the rest of the money they need. The field trip will cost a total of $386. Which inequality can be used to find p, the number of pies the class needs to sell in order to earn enough money to pay for the field trip?

• 5p + 75 ≤ 386

• 5p + 75 ≥ 386

• 75p + 5 ≥ 386

• 75p + 5 ≤ 386

Tags

7.10.A

Eliana purchased some pencils for $0.45 each. She also purchased a ruler for $1.60. Eliana spent more than $1.75 on the ruler and pencils. Which inequality can be used to find p, the number of pencils that Eliana could have purchased?

• 0.45p + 1.6 < 1.75

• 0.45p − 1.6 > 1.75

• 0.45p + 1.6 > 1.75

• 0.45p − 1.6 < 1.75

Tags

7.10.A

An inequality in one-variable is shown.
28x + 52 ≥ 1,200
Which problem situation could represent the inequality?

• Debbie sold 52 boxes of fruit for $28 each plus a bonus, x, for selling the boxes quickly. Find x, the least amount of bonus Debbie will earn if Debbie sold the fruit quickly and earned at least $1,200.

• Katrina earned 52 dollars an hour plus a weekly bonus of $28 for providing technical support at a local Internet Service Provider. Find x, the amount of hours Katrina must work to earn no more than $1,200.

• Marissa has $52 in her savings account. She earns $28 for each lawn she mows. Find x, the least number of lawns she will need to mow in order to have a total of at least $1,200 in her savings account.

• Edward had a balance of $52 in the bank. He added x dollars to his account last month. This week he deposited another $28. Find x, the amount Edward deposited in the bank last month if his total savings is now $1,200.

Tags

7.10.A

A student rode a bicycle fewer than 30 miles during a period of 5 days. The student rode 8 miles on Monday and x miles each day from Tuesday through Friday.

 

Which inequality represents all possible values of x?

• 4m  + 8 < 30

• 4m + 8 > 30

• 4m - 8 > 30

• 4m - 8 < 30

Tags

7.10.A

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

• x + y < 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y ≥ 20

• x + y ≤ 10

  2x + 3y > 20

• x + y < 10

  2x + 3y > 20

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66

• b + t > 15
  3b + 6t < 66

• 3b + 6t > 15
  b + t < 66

• 3b + 6t < 15
  b + t < 66