A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation?

Question

A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 15 to create a system that represents this situation?

Answer 1

The time it takes to dye x small rugs is 2x hours, and the time it takes to dye y medium rugs is 3y hours. Therefore, the total time it takes to dye x small rugs and y medium rugs is 2x + 3y hours.

We need an inequality that represents the condition that the total time must be less than 60 hours. That inequality is:

2x + 3y < 60

Therefore, the system of inequalities that represents this situation is:

x + y ≥ 15
2x + 3y < 60