Inequalities Application

A new tree you just planted will grow to be at most 35 feet tall. If it is currently 6 feet tall. Which of the following inequalities could be used to find all all the possible values of how many more feet, f, will it grow?

• 6 + x ≥ 35

• 6 + x > 35

• 6 + x < 35

• 6 + x ≤ 35

An unknown number decreased by 9 is at most 25. What is the number?

• x - 9 ≤ 25

• x - 9 < 25

• x - 9 > 25

You start a dog walking business. Each dog earns you $8. Which of the following inequalities could help you find all the possible values of d, the amount of dogs you will need to walk, to have more than $32?

The temperature for the day starts at 37 degrees and rises to at least 60 degrees.

Which of the following inequalities could be used to find all the possible values of t, the amount the temperature could rise?

• 37 + x > 60

• 37 + x ≥ 60

• 37 + x < 60

• 37 + x ≤ 60

Trisha and her three sisters to decide to purchase their mom a Christmas gift. They decide that everyone will contribute an equal amount, up to $60 per person. Which inequality will help find how much money will the sisters spend on their mom for Christmas?

• x ÷ 4 ≤ 60

• 4x ≤ 60

• x ÷ 4 ≥ 60

• 4x ≥ 60

Monica wants to spend at most $40 at the county fair. Entrance to the fair costs $15. She can spend d dollars on other things at the fair. Which inequality can be used to find the possible values of d?

• d − 15 > 40

• d − 15 < 40

• d + 15 ≥ 40

• d + 15 ≤ 40

Tucker lost fewer than 9 points. Which inequality represents the situation?

• p > 9

• p < 9

• p ≥ 9

• p ≤ 9

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

• 10x+15y≤480
  45x+25y≥250

• 10x+25y≤200
  15x+45y≤480

• 10x+25y>200
  15x+45y<480

• 10x+25y≥200
  15x+45y≤480

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

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