Question

opal makes $10 per hour working for a photographer. she also coaches a competitive soccer team for $10 per hour. opal needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. A. define the variables and write a system of inequalities to represent this solution. B. give one possible solution to describe how opal can meet her goals. explain how this solution works for opal. C. is (2,2) a solution, explain.

Answer 1

Hi there,

I hope you and your family are staying safe and healthy during this anomalous time.

A) Define the variables and write a system of inequalities to represent this solution.

Let's get started here with the question:

Let x = the number of hours for the photographer. Then let's have y = the hours for coaching

Thus, the system of inequalities looks like this:

`x + y \leq 20, 10x + 10y \geq 10`

B) Give one of the possible solutions to describe how Opal can meet her goal. Explain how this solution works for Opa.

I believe she will meet her goal if she works for 6 hours at the photographer's, then does 10 hours coaching; 8 hours at the photographer's then 10 hours of coaching

C) Is (2,2) a solution. Explain.

No, it is NOT a solution. When we graph the inequalities above, the point for (2,2) doesn't fall in the shaded region. As a result, she wouldn't be able to make as much money.

Happy to help! I wish you all the best this semester.

~Garebear