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

Answer:- x + y ≥ 15 (minimum number of rugs required)

- 2x + 3y < 60 (time constraint)

Explanation:

To represent the situation described, we can create a system of inequalities using the given information.

Let's start by identifying the time required to dye each rug:

- A small rug requires 2 hours for dyeing.

- A medium-size rug requires 3 hours for dyeing.

Next, let's define the variables:

- Let x represent the number of small rugs.

- Let y represent the number of medium rugs.

Based on the information provided, we know the following conditions must be met:

1. The dyers need to make at least 15 rugs: x + y ≥ 15. (This inequality represents the minimum number of rugs required.)

Now, let's consider the time constraint:

- The total time available is 60 hours.

To create the inequality representing the time constraint, we can calculate the total time required for dyeing the rugs:

- The time required for dyeing x small rugs is 2x hours.

- The time required for dyeing y medium rugs is 3y hours.

So, the total time required for dyeing the rugs is 2x + 3y hours.

To ensure the total time is less than 60 hours, we can add the following inequality to the system:

2. 2x + 3y < 60. (This inequality represents the time constraint.)

Therefore, the system of inequalities representing this situation is:

- x + y ≥ 15 (minimum number of rugs required)

- 2x + 3y < 60 (time constraint)