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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?

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jodeelhyn
Let x=small rugs and y=medium rugs. It takes 8 hours to dye a small rug, so you would write 8x. It takes 12 hours to dye a small rug, so you would write 12y. Those two would need to be added together. The dyer needs to dye at least 22 rugs in 240 hours, so you would need a less than or = to sign.
I'm not sure which choice has the line beneath, indicating that the sign is a "less than or equal to" sign, but the answer is gonna be either C or D.
8x+12y≤240, or 12y+8x≤240
Lanuel

Since the dyers must make at least 22 rugs in less than 240 hours, a system of inequality which represents this situation is: C. 8x + 12y < 240.

How to determine inequality?

First of all, we would assign variables to the small-size rug and medium-size rug as follows:

  • Let x be the small-size rug.
  • Let y be the medium-size rug.

Translating the word problem into an equation, we have;

A small-size rug requires 8 hours for dyeing: 8x.

A medium-size rug requires 12 hours for dyeing: 12y.

Since the dyers must make at least 22 rugs in less than 240 hours, a system of inequality which represents this situation is given by:

8x + 12y < 240.

Read more on inequalities here: https://brainly.com/question/24372553

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Complete 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 t 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?

A. 8x + 12y > 240

B. 12x + 8y > 240

C. 8x + 12y < 240

D. 12x + 8y < 240

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