Question

Who wants to rent a car rental car company charges $35 per day plus $.10 per mile driven rental company be charges $25 per day plus $.15 per mile driven how many miles driven will the price charge by each company be the same miles

Answer 1

What will the price be for you that number of miles

Answer 2

Let's denote \( x \) as the number of miles driven.

For the first car rental company, the total cost \( C_1 \) can be expressed as:
\[
C_1 = 35 + 0.10x
\]

For the second car rental company, the total cost \( C_2 \) is:
\[
C_2 = 25 + 0.15x
\]

To find the mileage at which both companies charge the same amount, we set the two equations equal to each other:
\[
35 + 0.10x = 25 + 0.15x
\]

Now, we can solve for \( x \). First, isolate the \( x \) terms on one side:
\[
35 - 25 = 0.15x - 0.10x
\]
\[
10 = 0.05x
\]

Next, solve for \( x \) by dividing both sides by 0.05:
\[
x = \frac{10}{0.05}
\]
\[
x = 200
\]

Therefore, the price charged by each company will be the same when \( 200 \) miles have been driven.

Answer 3

To find the price for both rental companies at 200 miles driven, we can substitute \( x = 200 \) into the cost equations for each company.

### For the first rental company:
\[
C_1 = 35 + 0.10 \times 200
\]
\[
C_1 = 35 + 20
\]
\[
C_1 = 55
\]

### For the second rental company:
\[
C_2 = 25 + 0.15 \times 200
\]
\[
C_2 = 25 + 30
\]
\[
C_2 = 55
\]

Thus, the price charged by each company when driving 200 miles will be **$55**.