Question

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week. Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work. Graph the inequalities. What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain. What is the maximum amount of money Lia can earn in 1 week? Explain.

Answer 1

Hey

your answer is (1) r+y<=15
r>=5
8r+12y>=120
(3) assuming she will work 15 hours, y = 15-r
so
8r + 12(15-r) >= 120
8r+180-12r>=120
-4r+180>=120
-4r >= -60
r <= 15
looks like she could work all 15 hours and still make 120 dollars
(4) r= 5 required hours in the restaurant then
8r + 12(15-r)= 160

Hoped I Helped