Word Problem

Question

Thrift rents a compact car for $32 per day, and General rents a similar car for $23 per day plus an initial fee of $54. For how many days d would it be cheaper to rent from General?

Answer 1

Let d = the number of days of renting the car.

 

32 * d is how much it would cost to rent from Thrift.

 

23 * d + 54 is how much it would cost to rent from General.

 

 

If we set these equal to each other, we can solve for the number of days (d) where the renter would "break even".

 

32 d = 23 d + 54

 

 

Subtract 23d from both sides.

 

9d = 54

 

 

Divide both sides by 9

 

d = 6

 

 

 

On day 6 it will cost the same to rent from Thrift ($32 * 6 = $192)

as it does to rent from General ($54 + $23 * 6 = $192)

 

In order for it to be cheaper to rent from General, we would need to rent the car at least 7 days.  

 

Check:  Thrift = $32 * 7 = $224

General = $54 + $23 * 7 = $215, definitely cheaper at 7 days.

 

Answer:  7 days.