Question

Fran brings home $225 per week working 15 hours of which she is able to save $40. Fran wants to have $1,400 saved at the end of 20 weeks. She may work up to 18 hours per week if she wants. She can save all of the money earned working the extra hours. Which of the following statements is true?
a.
Fran must work at least 15 hours per week to meet her goal.
b.
Fran must work at least 17 hours per week to meet her goal.
c.
Fran must work at least 18 hours per week to meet her goal.
d.
Fran will not be able to reach her goal.

Answer 1

Hourly pay = 225/15 = $15/hr. At h hours/week she saves 40 + 15(h−15) dollars/week. Over 20 weeks she saves 20[40 + 15(h−15)] ≥ 1400.

Solve: 20(40 + 15h − 225) ≥ 1400 → 20(15h − 185) ≥ 1400 → 300h − 3700 ≥ 1400 → 300h ≥ 5100 → h ≥ 17.

So she must work at least 17 hours/week. Answer: b.