Question:
Carlos will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $51 and costs an additional $0.08 per mile driven. The second plan has an initial fee of $46 and costs an additional $0.12 per mile driven.
For what amount of driving do the plans cost the same?
Answer:
Carlos needs to drive 125 miles for two plans to cost the same
Solution:
Let "x" be the number of miles driven
The first plan has an initial fee of $51 and costs an additional $0.08 per mile driven
Therefore,
First plan cost = 51 + 0.08(number of miles)
First plan cost = 51 + 0.08x --------- eqn 1
The second plan has an initial fee of $46 and costs an additional $0.12 per mile driven
Therefore,
Second plan cost = 46 + 0.12(number of miles)
Second plan cost = 46 + 0.12x -------- eqn 2
For what amount of driving do the plans cost the same?
Eqn 1 = eqn 2
51 + 0.08x = 46 + 0.12x
0.12x - 0.08x = 51 - 46
0.04x = 5
Divide both sides by 0.04
x = 125
Therefore, Carlos needs to drive 125 miles for two plans to cost the same