Question

Tom wishes to rent a car for a day. Enterprise Car Rental wants $22 per day and $0.15 per mile, while Budget Car Rental wants $18 per day and $0.19 per mile. After how many miles would the price to lease from Budget exceed the price to lease from Enterprise?

Answer 1

After 100 miles

Explanation:

Step 1: Write an equation to represent Tom's rental cost cost at Enterprise Car Rental:

• The $22 per day is a flat fee, meaning Tom would pay this amount, even if he drove 0 miles.
• Along with the $22 flat fee, he pays $0.15 per each mile driven.
• We can allow m to represent the number of miles.

Thus, Tom's rental cost at Enterprise Car Rental is given by:

E(m) = 0.15m + 22

Step 2: Write an equation to represent Tom's rental cost at Budget Car Rental:

• The $18 per day is also a flat fee, meaning Tom would pay this amount, even if he drove 0 miles.
• Along with the $18 flat fee, he pays $0.19 per each mile driven.
• We can allow m to represent the number of miles.

Thus, Tom's rental cost at Budget Car Rental is given by:

B(m) = 0.19m + 18

Step 3: Determine after how many miles would his rental cost at Budget Car Rental exceed his rental cost at Enterprise Car Rental:

We can determine after how many miles would Tom's rental cost at Budget Car Rental exceed his rental cost at Enterprise Car Rental by making B(m) greater than E(m) and solving for m:

B(m) > E(m)

(0.19m + 18 > 0.15m + 22) - 18

(0.19m > 0.15m + 4) - 0.15m

(0.04m > 4) / 0.04

m > 100

Thus, the price to lease from Budget would exceed the price to least from Enterprise after 100 miles.