Question

You and your friend each start a car-washing service. You spend $25 on supplies and charge $10 per car. Your friend spends $55 on supplies and charges $13 per car. How many cars do you have to wash to earn the same amount of money as your friend?

Answer 1

10 cars

Explanation:

The function for your earnings in terms of cars washed is f(x) = 10x - 25 (charges 10 per car and the supplies costed $25)

The function for your friend's earnings in terms of cars washed is g(x) = 13x - 55 (charges 13 per car and the supplies costed $55)

The problem asks us how many cars do you have to wash to earn the same amount of money as your friend?

To solve this, you would have to equal both functions and solve for x:

`f(x)=g(x)\\10x-25=13x-55\\-25+55=13x-10x\\30=3x\\10=x`

x = 10, therefore you'd have to wash 10 cars to earn the same amount of money as your friend (who would also have to wash 10 cars)

Answer 2

Set both equations equal to each other to solve for x ( number of cars).

10x -25 = 13x - 55

Subtract 10x from each side:

-25 = 3x-55

Add 55 to each side:

30 = 3x

Divide both sides by 3:

x = 30/3

x = 10

They will need to wash 10 cars.