Alice is working 2 jobs to save up money for a trip. She works at the ice cream shop for $9 an hour and babysitting for $12 an hour. She needs to earn at least $200 per week and can only work 20 hours per week. Write a system of inequalities to model the number of hours she needs to work at the ice cream shop, x, and the number of hours babysitting, y. Then choose the graph of that system below.

Question

Alice is working 2 jobs to save up money for a trip. She works at the ice cream shop for $9 an hour and babysitting for $12 an hour. She needs to earn at least $200 per week and can only work 20 hours per week. Write a system of inequalities to model the number of hours she needs to work at the ice cream shop, x, and the number of hours babysitting, y. Then choose the graph of that system below.

Answer 1

x + y ? 20

9x + 12y ? 200

whatever graph they give you, there should be one with the region below x+y = 20 shaded in AND the region above 9x + 12y = 200 shaded in.
It should look something like this:

http://www.wolframalpha.com/input/?i=plot+x+%2B+y+%3D+20+,+9x+%2B+12y+%3D+200

with the shaded in area as I noted.

Answer 2

To model the number of hours Alice needs to work at the ice cream shop (x) and the number of hours babysitting (y), we can set up the following system of inequalities:

1) Alice needs to earn at least $200 per week:
9x + 12y ≥ 200

2) She can only work 20 hours per week:
x + y ≤ 20

So, the system of inequalities is:
9x + 12y ≥ 200
x + y ≤ 20

Now, let's choose the graph of that system below.