Question

Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at different rates and then sets up the equation 0.22m+7.20=0.1m+8.40 to find out after how many miles, m, the companies will charge the same amount. What is the difference in per-mile costs for the two companies?

Answer 1

The difference in per-mile costs for the two companies is $0.12

Explanation:

Gabi sets up the equation
`0.22m+7.20=0.1m+8.40` to find out after how many miles, m, the companies will charge the same amount.

The first company charges
`c_1=0.22m+7.20` for m miles driven.

The second company charges
`c_2=0.1m+8.40` for m miles driven.

In both these functions, numbers 7.20 and 8,40 represent the initial fee the companies charge.

Numbers 0.22 and 0.1 represent per-mile costs.

Thus, the difference in per-mile costs is
`0.22-0.1=0.12`

Another way to solve this problem is to find the cost per mile driven for each company:

1. Cost per-mile 1st company

`c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22`

2. Cost per-mile 2nd company

`c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1`

3. Difference:

`0.22-0.1=0.12`