Question

A company offers four plans for customers who want to rent DVDs and video games. The costs of the plans can be modeled by a linear function that combines a one-time membership fee with a per disc rental rate. The table shows the total costs, including membership fees, for a person who rents 1, 2, and 5 discs in a month.

Cost of Repairs
Discs rented
Plan A
Plan B
Plan C
Plan D
1
$14
$12
$10
$12
2
$17
$16
$15
$21
5
$26
$28
$30
$48

Which plan has the smallest one-time membership fee?
plan A
plan B
plan C
plan D

Answer 1

Plan D.

Work: For each plan cost = m*(discs) + b. From 1 and 2 discs m = cost(2)-cost(1), then b = cost(1) - m.
- A: m=3, b=14-3=11
- B: m=4, b=12-4=8
- C: m=5, b=10-5=5
- D: m=9, b=12-9=3

Smallest membership fee is $3 (Plan D).