Question

A company dyes two sizes of rugs. A small rug requires 8 hours for dyeing and a medium-size rug requires 12 hours for dyeing. The dyers have to make at least 22 rugs, and they must do it in less than 240 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 22 to create a system that represents this situation?

8x + 12y > 240
12x + 8y > 240
8x + 12y < 240
12x + 8y < 240

Answer 1

c

Explanation:

Answer 2

8x + 12y < 240

Explanation:

If x equals the number of small rugs and y equals the number of medium rugs dyed, we would need to multiply both variables by the number of hours taken to dye each sized rug. It takes 8 hours to dye a small rug (8x), and 12 hours to dye a medium rug (12y).

Then, to find the total number of hours they dye them in, add the terms together.

8x + 12y

The company must dye the rugs in less than 240 hours, so we will use a 'less than' (inequality) sign (it cannot be 240, or any more than 240).

8x + 12y < 240