Question

Car Wash A theater group is having a carwash fundraiser. The liquid soap costs $34 and is enough to wash 40 cars. Each car is charged $5.

a. If c is the total number of cars washed and p is the profit, which is the independent variable and which is the dependent variable?

b. Is the relationship between c and p a function? Explain.

c. Write an equation that shows this relationship.

d. Find a reasonable domain and range for the situation.

Answer 1

a. If c is the total number of cars washed and p is the profit

The profit depends on the total number of cars washed.

So profit P is the dependent variable and C is the independent variable

(b) yes, the relationship between c and p a function

Because for each input for c, there will be an unique output for P

(c) C is the number of cars

Each car charged is $5

So C cars charged is 5C

The liquid soap costs $34 and is enough to wash 40 cars. So we subtract 34

Hence Profit P = 5c - 34

The equation is P = 5c - 34

(d) The liquid soap costs $34 and is enough to wash 40 cars

So number of cars is 0 to 40

0<=c <=40

soap costs $34

so profit is above 34

When cars = 40 then profit is 5(40) - 34= 166

So profit lies between 34  and 166

34<= P<= 166