Question

Greg is opening a car wash. He estimates his cost equation as C = 9000 + 0.09x and his revenue equation as R = 1.75x, where x is the number of cars washed in a six-month period. Find the numbers of cars that must be washed in a six-month period for Greg to make a profit.

Answer 1

In order to make a profit, the revenue needs to be greater than the cost.

So we can write the following inequality and solve it for x:

`\begin{gathered} R>C \\ 1.75x>9000+0.09x \\ 1.75x-0.09x>9000 \\ 1.66x>9000 \\ x>(9000)/(1.66) \\ x>5421.69 \end{gathered}`

So the number of cars needs to be 5422 cars so Greg starts making a profit.