Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: Solving Story Problems Involving Inequalities

Q1:

Anthony earns $6.75 an hour waiting on tables. He is saving money to buy a new video game which costs $27. Write an inequality to find how many hours Anthony must work to buy the game, and then solve it.

  • A 2 7 π‘₯ ≀ 6 . 7 5 , π‘₯ ≀ 1 4
  • B 6 . 7 5 π‘₯ ≀ 2 7 , π‘₯ ≀ 4
  • C 2 7 π‘₯ β‰₯ 6 . 7 5 , π‘₯ β‰₯ 1 4
  • D 6 . 7 5 π‘₯ β‰₯ 2 7 , π‘₯ β‰₯ 4
  • E 6 . 7 5 π‘₯ > 2 7 , π‘₯ > 4

Q2:

Matthew ran 600 meters in 90 seconds, while Sophia was at least 9 seconds ahead of him. Write an inequality to represent the time Sophia finished the 600-meter run.

  • A π‘₯ ≀ 9 9
  • B π‘₯ β‰₯ 8 1
  • C π‘₯ β‰₯ 9 9
  • D π‘₯ ≀ 8 1
  • E π‘₯ < 9 0

Q3:

Michael wants to purchase a precision balance for $340. He has already saved $113 and can save $28 every week. Write an inequality that can be used to determine the number of weeks left for Michael to save at least $340.

  • A 1 1 3 π‘₯ + 2 8 β‰₯ 3 4 0
  • B 2 8 π‘₯ + 1 1 3 ≀ 3 4 0
  • C 1 1 3 π‘₯ + 2 8 ≀ 3 4 0
  • D 2 8 π‘₯ + 1 1 3 β‰₯ 3 4 0
  • E 2 8 π‘₯ + 1 1 3 > 3 4 0

Q4:

Michael finds two plumbers online: the first charges $20 per hour of labor, while the second charges a fixed charge of $40 per job plus an hourly labor charge of $15. After how many hours will the second plumber be cheaper than the first?

  • A2 hours
  • B4 hours
  • C6 hours
  • D8 hours
  • E5 hours

Q5:

Sophia finds two landscape gardeners online: the first charges a fixed fee of $20 per job plus $15 per hour for labor, while the second charges a fixed fee of $90 but only $5 per hour for labor. After how many hours will the second gardener be cheaper than the first?

Q6:

You are choosing between two different window-washing companies. The first charges $ 5 per window, while the second charges a base fee of $ 4 0 plus $ 3 per window. How many windows would you need to have for the second company to be preferable?

  • Amore than 15 windows
  • Bmore than 5 windows
  • Cmore than 8 windows
  • Dmore than 20 windows
  • EMore than 10 windows

Q7:

When hired at a new job selling electronics, you are given two pay options:

  • Option A: a base salary of $ 2 0 0 0 0 a year with a commission of 1 2 % of your sales
  • Option B: a base salary of $ 2 6 0 0 0 a year with a commission of 3 % of your sales

How many dollars’ worth of electronics would you need to sell for option A to produce a larger income?

  • Amore than $ 4 0 0 0 0 worth of electronics
  • Bmore than $ 5 1 1 1 1 1 . 1 1 worth of electronics
  • Cmore than $ 3 0 6 6 6 6 . 6 7 worth of electronics
  • Dmore than $ 6 6 6 6 6 . 6 7 worth of electronics

Q8:

When hired at a new job selling electronics, you are given two pay options:

  • Option A: a base salary of $ 1 0 0 0 0 a year with a commission of 9 % of your sales.
  • Option B: a base salary of $ 2 0 0 0 0 a year with a commission of 4 % of your sales.

How many dollars’ worth of electronics would you need to sell for Option A to produce a larger income?

  • Amore than $ 2 3 0 7 6 9 . 2 3 worth of electronics
  • Bmore than $ 6 0 0 0 0 0 worth of electronics
  • Cmore than $ 7 6 9 2 3 . 0 8 worth of electronics
  • Dmore than $ 2 0 0 0 0 0 worth of electronics