help please

Audrey is working two summer jobs, making $12 per hour babysitting and making
$8 per hour washing cars. In a given week, she can work no more than 16 total
hours and must earn no less than $160. Also, she must work at least 2 hours
washing cars. If a represents the number of hours babysitting and y represents
the number of hours washing cars, write and solve a system of inequalities
graphically and determine one possible solution.

Answer :

Answer: (8, 8)

Step-by-step explanation:

To solve this problem, we need to set up the following system of inequalities:

1. a + y ≤ 16 (total hours worked cannot exceed 16 hours)

2. 12a + 8y ≥ 160 (total earnings must be at least $160)

3. y ≥ 2 (she must work at least 2 hours washing cars)

To graph these inequalities, plot the lines:

a + y = 16 (dotted line passing through points (16,0) and (0,16) )

12a + 8y = 160 (dotted line passing through points (13.33,0) and (0,20) )

y = 2 (solid line passing through point (0, 2) )

The feasible region will be the triangle formed by the intersection of these lines. One possible solution within this region could be a = 8 hours babysitting and y = 8 hours washing cars.

Hope this helps!

View image a18600079
View image a18600079

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