I can’t figure out the answer to this problem

Question

Alexa is working two summer jobs, making 22$ Per hour tutoring and making $13 per hour landscaping. In a given week, she can work at most 15 total hours and must earn no less than $260. If x represents the number of hours tutoring and y represents the total number of landscaping, write and solve a system of inequalities graphically and determine one possible solution

Answer 1

Hayden,

First assign variables:

x =number of hours spent tutoring

y =number of hours spent landscaping

Alexa can't work more than 15 hours, so x+y ≤15.

Also, she needs to make at least $260 per week, so use the hourly rates to get 22x +13y ≥260.

You can graph these in this form on paper by using intercepts or on Desmos.com just like this. You'll need to convert them to slope-intercept form to graph them on a regular graphing calculator.

Either way, look for the area where the shaded parts overlap. There are a number of clear coordinates in that area, like (12,2) or (10,4). Anything there should work.

If x=12 and y=2, for example, x+y is 15 hours, and 12(22) +2(13) = $290. Alexa works her maximum amount of hours, and she makes more than her minimum!

I hope this helps; please let me know if you have a question, and have fun mathing!

Liz Z.