Question

In order to save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother told him he can work no more than 15 hours in order to keep up with his homework. If Tom would like to make at least $75 to cover prom expenses, help him determine combinations of hours he can work between these two jobs.

a. Write and graph a system of inequalities.



b. Write two possible solutions:
I.
ii.​

Answer 1

6x + 7.50y ≥ 75

Explanation:

Let x = # of hours he walks the dog

y = # of hours he washes cars

We also know that he cannot have any negative hours, so 2 lines that we need to graph will be y = 0, with everything above this line shaded in, and x = 0, with everything to the right of this line shaded in and these lines will be solid because you can have 0 hours.

Another equation will be x + y ≤ 15. We graph the line, which will be solid, y = -x + 15, and shade everything to the left of this line.

The last equation will be 6x + 7.50y ≥ 75. We graph this solid line, y ≥ (-6x + 75)/7.50 & shade everything to the right of this line. Any point inside the area shaded in by all 4 equations will be an answer. I'll leave this up to you.

Hope this helps!