Question

Two car rental companies are running specials this month. At DriveAway's Rentals, customers can pay a $30 rental fee for a sedan and $15 for each day of the rental. At Harry's Rent-a-Car, customers can pay a $40 rental fee for a sedan and $10 for each day of the rental. The costs for the two car rentals are shown on the graph below. How many days must a car be rented for the cost of both car rentals to be the same?

Answer 1

The costs for DriveAway's Rentals and Harry's Rent-a-Car are the same after renting for 2 days.

Let x be the number of days a car is rented. The total cost for DriveAway's Rentals is given by:

`\[ C_{\text{DriveAway}}(x) = 30 + 15x \]`

And for Harry's Rent-a-Car:

`\[ C_{\text{Harry's}}(x) = 40 + 10x \]`

To find when the costs are the same, set the two expressions equal to each other and solve for x:

30 + 15x = 40 + 10x

Combine like terms:

5x = 10

Divide by 5:

x = 2

So, the costs will be the same after renting for 2 days. After 2 days, the total cost for DriveAway's Rentals
`(\( C_{\text{DriveAway}} \))` and Harry's Rent-a-Car
`(\( C_{\text{Harry's}} \))` will be equal.