Question

A piano instructor charges students a one-time fee for sheet music and an hourly rate for lessons. The graph below shows the total cost for a student who has taken x lessons.

Total Cost of Piano Lessons

A graph has lessons on the x-axis, and dollars on the y-axis. Points are at (1, 50), (2, 80), (3, 110), (4, 140), (5, 170).

To increase her number of students, the instructor put a coupon in the local paper offering to waive the one-time fee for new students. What is the value of the coupon?
$14
$20
$30
$50

Answer 1

The cost increases by $30 per lesson (80−50=30), so the hourly rate is $30. Extrapolating back to 0 lessons: 50−30 = $20. The one-time fee is $20, so the coupon value is $20.