Question

Car Wash A theater group is having a carwash fundraiser. The liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$. 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) Independent variable is "c"

Dependent variable is "p"

B) Yes, it's a function

C) p = 7c - 31

D)domain of the function: 0 ≤ c ≤ 40

Range of the function: 0 ≤ p ≤ 249

Explanation:

A) c is the total number of cars washed and p is the profit. The profit depends on the total number of cars washed. Hence, profit(p) is the dependent variable while "c" is independent variable

B) Yes it's a function because for each number of cars washed, there is a distinct value of profit made.

C) We are told that the liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$.

$31 is cost to wash one car. Thus profit made per car is;

p = 7c - 31

D) The cost of $31 liquid soap is enough to only wash a maximum of 40 cars. This means the domain for the cars is from 0 cars to 40 cars

Thus;

domain of the function is 0 ≤ c ≤ 40

The profit function is given in answer C above as p = 7c - 31.

Now, if 0 cars are washed they will make zero profit but if 40 cars are washed then;

p = 7(40) - 31

p = 280 - 31

p = 249

Range of the function: 0 ≤ p ≤ 249