Question

Rental Company A charges a fee of $80 plus $35 per day to rent a mid-sized car. Rental Company B charges a fee of only $30 for a mid-sized car but adds $45 per day to the total rental charge.

For a certain number of rental days, the amounts that the two companies charge to rent a mid-sized car will be equal. What is the total charged by each company for that number of rental days?
$240
$255
$430
$480

Answer 1

Let \( d \) represent the number of rental days.

The total cost to rent a mid-sized car from Rental Company A can be expressed as:
\[
\text{Cost}_A = 80 + 35d
\]

The total cost to rent a mid-sized car from Rental Company B can be expressed as:
\[
\text{Cost}_B = 30 + 45d
\]

To find the number of rental days where the costs are equal, we set the two equations equal to each other:
\[
80 + 35d = 30 + 45d
\]

Now, we can solve for \( d \):

1. Subtract \( 30 \) from both sides:
\[
50 + 35d = 45d
\]

2. Subtract \( 35d \) from both sides:
\[
50 = 10d
\]

3. Divide both sides by \( 10 \):
\[
d = 5
\]

Now that we have found \( d = 5 \), we can calculate the total cost from either company.

Using Rental Company A:
\[
\text{Cost}_A = 80 + 35 \cdot 5 = 80 + 175 = 255
\]

Using Rental Company B:
\[
\text{Cost}_B = 30 + 45 \cdot 5 = 30 + 225 = 255
\]

Both companies charge \( 255 \) for 5 rental days.

Thus, the total charged by each company for that number of rental days is:
\[
\boxed{255}
\]