Question

Wyatt is working two summer jobs, making $8 per hour walking dogs and making $14 per hour tutoring. In a given week, he can work a maximum of 13 total hours and must earn a minimum of $140. If x represents the number of hours walking dogs and y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Please make 2 inequalities using slope intercept form.

Answer 1

One inequality will be about the number of hours Wyatt works, and the other about how much money he makes based on the number of hours he works at each job.

x represents dog walking, y represents tutoring

Hours inequality:

x + y ≤ 13

y ≤ -x + 13

Income inequality:

8x + 14y ≥ 140

14y ≥ -8x + 140

y ≥ -4/7x + 10

To determine the solution to these inequalities, we can set them equal to each other and solve for x, then use our value of x to solve for y.

-x + 13 = -4/7x + 10

-x +3 = -4/7x

3 = 3/7x

x = 7

y = -x + 13

y = -7 + 13

y = 6

The solution is (7, 6), where Wyatt works 7 hours walking dogs and 6 hours tutoring.