Question

Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. If she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. How much more does Charlotte earn per hour on the weekends than she earns during the week? Round to the nearest cent.

Answer 1

Charlotte earns 2.30

Answer 2

X: earn per  hour during the week
y: earn per hour during the weekend

13x + 14y = 250.90
15x + 8y = 204.70

Multiply the first equation by 4 and the second equation by 7

52x + 56y = 1003.6
105x + 56y = 1432.90

Subtract the first equation from the second:

 53x = 429.30

x = 429.30/ 53
x = 8.10

Solve any of the equation for y:

15x + 8y = 204.70

y = [204.70 - 15(8.10)]/8 = 10.40

y - x = 10.40 -8.10 = 2.30

Answer: she earns $2.30 per hour more during the weekend than during the week.