4.06 Question 6 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?

2x + 3y < 60
3x + 2y < 60
2x + 3y > 60
3x + 2y > 60

If we are to make x small rugs, each of which takes 2 hours to dye, then the total time taken to dye the small rugs is 2x. Similarly for the y large rugs which each take 3 hours to dye, the total time for dyeing the large rugs is 3y. Therefore the total for all sizes of rugs is 2x + 3y. Finally, we have a maximum of 60 available hours for the dyeing, so the total time cannot exceed 60, and the final inequality is

2x + 3y < 60

Step-by-step explanation:

Option (1) is correct.

Option (1) is correct.2x + 3y < 60  inequalities can be paired with x + y ≥ 15 to create a system that represents the given situation.

Option (1) is correct.2x + 3y < 60  inequalities can be paired with x + y ≥ 15 to create a system that represents the given situation.Step-by-step explanation:

 Given : A company dyes two sizes of rugs A and B.

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.

we have to find an  inequalities can be paired with x + y ≥ 15 to create a system that represents the given situation.

The dyers need to make at least 15 rugs.

Let x equal small rugs and

Let x equal small rugs and y equal medium rugs

This can be represented by the equation x + y ≥ 15

Also,  The small rug requires 2 hours for dyeing and the medium-size rug requires 3 hours for dyeing and they must do it in less than 60 hours

Then to dye x small rugs the time taken is 2x

Then to dye x small rugs the time taken is 2xand  to dye y medium rugs the time taken is 3y

and total time given to  dye is less than 60 hours

This can be represented by the equation 2x + 3y < 60

2x + 3y < 60Thus, Option (1) is correct.

2x + 3y < 60Thus, Option (1) is correct.2x + 3y < 60  inequalities can be paired with x + y ≥ 15 to create a system that represents the given situation.

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