Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at differ

Question

2 months ago

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Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at differ

ent 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?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-08T05:22:13+03:00

Answer:

The cost difference per mile between the two companies is $0.12.

Step-by-step explanation:

Gabi formulates the equation $0.22m+7.20=0.1m+8.40$ to determine after how many miles, denoted as m, the charges of both companies will be equal.

The first company levies $c_1=0.22m+7.20$ for m miles traveled.

The second company's charge for the same m miles is $c_2=0.1m+8.40$ .

In these equations, the figures 7.20 and 8.40 signify the initial fees the companies impose.

The values 0.22 and 0.1 represent the respective costs per mile.

As such, the disparity in per-mile charges amounts to $0.22-0.1=0.12$ .

An alternative method to tackle this problem is by calculating the per-mile rate for each company:

1. Cost per mile for the first 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 for the second 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. The difference:

$0.22-0.1=0.12$