Question

Alice is working two jobs to save up money for a trip. She works at the ice cream shop for eight dollars an hour and babysitting for $11 an hour. She needs to earn at least $125 per week and can only work 15 hours per week. Write a system of inequalities to represent the number of hours she needs to work at the ice cream shop, x, and the number of hours babysitting, y. What’s the graph?

a) 8x+11y≥125, x+y≤15
b) 8x+11y≤125, x+y≥15
c) 8x+11y≤125, x+y≤15
d) 8x+11y≥125, x+y≥15

Answer 1

The correct system of inequalities for Alice's situation is option a) 8x + 11y ≥ 125, x + y ≤ 15. This represents the minimum earnings and maximum hours she can work across her two jobs.

Step-by-step explanation:

The problem you're describing involves creating a system of inequalities to represent the number of hours Alice needs to work at an ice cream shop (x) and babysitting (y) to meet her financial goals. The first inequality, 8x + 11y ≥ 125, shows that the total earnings from both jobs should be at least $125. The second inequality, x + y ≤ 15, represents the constraint that Alice can work a combined total of no more than 15 hours per week.

To visualize this, we would graph these two inequalities on a coordinate plane, where the shaded region would represent all the possible combinations of hours Alice can work at both jobs while meeting her requirements.

The correct answer to the given situation is option a:
8x + 11y ≥ 125, x + y ≤ 15.