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 gallon 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

Josh would need to purchase 20 gallons of gas for the cost to be the same at each car wash

Explanation:

We need to model both car wash's costs. The Quik-Clean Car Wash charges $15 for a car wash plus $2.50 per gallon for unleaded gasoline. If x is the number of gallons of unleaded gasoline. the total charges of this store are:

C1=15+2.5*x

The Mighty Clean Car Wash charges $10 for a carwash plus $2.75 per gallon for unleaded gasoline. Following the same procedure, their costs are:

C2=10+2.75*x

Josh wants to know how many gallons of gas will make both businesses charge the same. Equating both equations:

15+2.5*x=10+2.75*x

Simplifying:

-0.25x=-5

Solving:

x=-5/(-0.25)=20

Josh would need to purchase 20 gallons of gas for the cost to be the same at each car wash