Suppose you have a job teaching swimming lessons and get paid $6 an hour. you also have job as cashier and get paid $8 and hour. if you cannot more than 15 hour a week what are the number of hours you can work at each job and still make at least $100?

This is a system of equations problem.

L =  Hours of Swim Lessons
C = Hours as Cashier

L + C = 15        This is an equation for working 15 hours total.
so
L = 15-C

6L + 8C = 100   This is an equation for making at least $100.
so
6 (15-C) + 8C = 100    *You substituted 15-C for L here
90 - 6C + 8C = 100      Distribute
90 + 2C = 100
2C = 10
C = 5          You can work 5 hours as a cashier

L + C = 15
L + 5 = 15
L = 10          You can work 10 hours teaching swimming lessons.

If you want to make EXACTLY $100 you would work 5 hours as cashier and 10 hours teaching swimming lessons.

HOWEVER, the question says AT LEAST $100 and NOT MORE than 15 hours per week. Since you make more money as a cashier, any work over 5 hours will help you make over $100.

As long as you work at least 5 hours as a cashier and any remaining hours teaching swimming lessons, you will make over $100.

5 cashier, 10 swimming
6 cashier, 9 swimming
7 cashier, 8 swimming...

Mr. Pacey
JH/HS Social Studies Teacher
(but I've also helped with Math Team for JH & HS)