Question

A car rental company charges $35 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $25 per day and $0.75 for every mile driven. What is the number of miles at which both companies change the same amount for a one-day rental?


25 miles


55 miles


35 miles


40 miles

Answer 1

To find the number of miles at which both rental companies charge the same amount for a one-day rental, we can set up an equation based on the costs of each company.

Let \( x \) be the number of miles driven.

**Cost for the first rental company:**
\[
\text{Cost}_1 = 35 + 0.50x
\]

**Cost for the second rental company:**
\[
\text{Cost}_2 = 25 + 0.75x
\]

We want to find the value of \( x \) where both costs are equal:
\[
35 + 0.50x = 25 + 0.75x
\]

Now, let's solve for \( x \).

1. Subtract \( 0.50x \) from both sides:
\[
35 = 25 + 0.25x
\]

2. Now, subtract 25 from both sides:
\[
10 = 0.25x
\]

3. Finally, divide by 0.25:
\[
x = \frac{10}{0.25} = 40
\]

Thus, the number of miles at which both companies charge the same amount for a one-day rental is **40 miles**.