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.

Question

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: \[ \boxed{255} \]