Question

The Math Club is holding a car wash to raise money for new calculators for the Math Team. They had to go out and buy soap, buckets, towels and more which cost a total of $72. Other clubs told them to expect to make $8 per vehicle (since some people will pay more and some will pay less.)a. Write an equation for their Profit in terms of how many vehicles they wash and their money spent on supplies.b. How many vehicles do they have to wash in order to break even on the supplies they bought? c. How many vehicles do they have to wash in order to make the $1000 profit they need to buy the calculators?

Answer 1

In this problem, we want to figure out what type of profit can be made by holding a carwash as a fundraiser.

To do the fundraiser, however, they must spend money on supplies.

Part A:

Let the total cost for supplies be represented by -$72, since it is money being spent by the team.

Let x represent the number of cars washed at a price of $8.

We can create the following equation:

`\begin{gathered} \text{ Profit}=\$8*(\text{ cars washed\rparen}-\$72 \\ y=8x-72 \end{gathered}`

Part B:

We want to know how many cars they must wash in order to make back the money spent on supplies, also known as "breaking even." To do this, the next amount should be exactly $0.

Set the equation equal to 0 and solve for x, the number of cars:

`0=8x-72`

Add 72 to both sides:

`72=8x`

Divide by 8 on both sides:

`9=x`

The group should was 9 cars to break even.

Part C:

If the team want to make a net profit if $1000, we can follow the same procedures. This time, let the equation be equal to $1000:

`1000=8x-72`

Add 72 to both sides:

`1072=8x`

Divide by 8 on both sides:

`134=x`

The team should wash 134 cars to earn $1000 in profit to buy the calculators.