Question

2. A rental car company charges $40.00 plus $0.10 per mile. Another company charges $25.00 plus $0.25 per mile. How many miles would you have to drive in order for the costs to be equal?

Answer 1

`\begin{gathered} x=\text{ number of miles } \\ Cost_{company\text{ A}}=40.00+0.10x \\ \text{Cost}_{company\text{ B}}=25.00+0.25x \\ Cost_{company\text{ A}}=\text{Cost}_{company\text{ B}} \\ 40.00+0.10x=25.00+0.25x \\ AFTER\text{ REORGANIZING} \\ 0.10x-0.25x=25.00-40.00 \\ -0.15x=-15 \\ x=(-15)/(-0.15) \\ x=100 \\ CHECKING \\ Cost_{company\text{ A}}=40.00+0.10(100) \\ Cost_{company\text{ A}}=40.00+10.00 \\ Cost_{company\text{ A}}=50.00 \\ \text{Cost}_{company\text{ B}}=25.00+0.25(100) \\ \text{Cost}_{company\text{ B}}=25.00+25.00 \\ \text{Cost}_{company\text{ B}}=50.00 \\ \text{both costs are equal, so you have to drive 100 miles in order for the costs be equal} \end{gathered}`