Question

Use Demos Graphing Calculator

Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising
horses and $10 an hour cleaning stalls. Because Rob is a full-time student, he can
work no more than 12 hours per week. However, he must make at least $60 per
week.

Which of the following is a possible solution for this system of inequalities?

A. 1 hour exercising and 1 hour cleaning

B. Two hours exercising and five hours of cleaning

C. Seven hours of exercising and eight hours of cleaning

D. Two hours exercising and eight hours cleaning

Answer 1

D. Two hours exercising and eight hours cleaning

Explanation:

Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising horses and $10 an hour cleaning stalls. Because Rob is a full-time student, he can work no more than 12 hours per week. However, he must make at least $60 per week.

x = hrs. exercising horses

y = hrs. cleaning stalls

Equations:

Hours he can work per week:

x + y ≤ 12

Amount of money he can make per week:

5x + 10y ≥ 60

Now, graph your equations into desmos.

As you can see in the graph, the correct answer is D (2, 8)

Check your answer by hand:

x + y ≤ 12

2 + 8 ≤ 12

10 ≤ 12

This statement is correct

5x + 10y ≥ 60

5(2) + 10(8) ≥ 60

10 + 80 ≥ 60

90 ≥ 60

This statement is correct

Therefore, the correct answer is D

Hope this helps!