Question

The Quik-Clean Car Wash charges $15 for a car wash plus $2.50 per gallon for unleaded gasoline. The Mighty Clean Car Wash charges $10 for a carwash plus $2.75 per for unleaded gasoline. Josh is comparing the cost of having his car wash plus filling up his tank with gas at each business. How many gallons of gas would he need to purchase for the cost to be the same at each car wash?

Answer 1

The indifference point is 20 gallons.

Explanation:

Giving the following information:

Quik-Clean Car Wash:

$15 for a car wash plus $2.50 per gallon for unleaded gasoline.

Mighty Clean Car Wash:

$10 for a carwash plus $2.75 per for unleaded gasoline.

First, we need to structure the total cost formula:

Quik-Clean= 15 + 2.5x

Mighty Clean= 10 + 2.75x

x= gallon of gasoline

Now, we equal both formulas and isolate x:

15 + 2.5x = 10 + 2.75x

5 = 0.25x

20 = x

The indifference point is 20 gallons.

Prove:

Quik-Clean= 15 + 2.5*20= $65

Mighty Clean= 10 + 2.75*20= $65