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.