Question

The Middle Grades Math Club needs to raise money for its spring trip to Washington, D.C., and for its Valentine’s Day dance. The club members decided to have a car wash to raise money for these projects. The club treasurer provided the following information: • Thetotalcostofsponges,rags,soap,buckets,andothermaterialsneededwillbe$117.50. • Theusualchargeforwashingonecaris$4.00. As a member of the club, your job is to produce a mathematical analysis of this situation that includes making a table and a graph to answer the following questions: 1.Howmuchmoneywouldtheclubraiseifthememberswashed0,1,2,3,or4cars? _________ _____________ 10 cars? _____________ 50 cars? ____________ 100 cars? ______________ How can you use your table to answer these questions? _________________________________ How can you use your graph to answer these questions? _________________________________ 2. (a) If no cars are washed, what happens to the club’s finances? How is this situation shown on the graph? _________________________ On the table? ________________________________ (b) With every car washed, what is the change in the amount of money earned? _______________ How is this change shown on the graph? _____________ On the table? _________________ (c) Write a general rule to use to determine how much money is raised for any number of cars. How is the information you identified for parts a and b related to the rule you wrote? _________________________________________________________________________________ 3. How many cars must the members wash to “break even”?_________________________________ 4. How many cars must the members wash to raise enough money for— • The trip to Washington—estimated cost, $875? _________________________________________ • The Valentine’s Day dance—estimated cost, $350? _____________________________________ 5. Realistically, can the car wash raise enough money for both of these activities? _____________ Explainwhyorwhynot.

Answer 1

A.

Cars            Amount

0 cars          $-117.50

1 car             $-113.50

2 cars          $-109.50

3 cars           $-106.50

4 cars           $-102.50

10 cars          $-77.50

50 cars         $82.50

100 cars        $282.50

I do not know what graph you have but, you can see how much money you will make because it will form a straight line on the graph. As long as you continue the line, you will be able to see how many cars you have to clean to make a certain amount of money. Same is for the table.

B.

The change in the amount of money earned with each car is $4.00

The change on the graph is shown by the increasing slope.

C.

The number of cars that need to be washed can be seen by using the formula y=4x-117.5

The information from part a and b is used to show that there is a constant change (slope) and that more money is made by washing more cars.

3. The members need to wash 30 cars (rounded up from 29.375) to break even.

4.  The members would have to wash 249 cars (rounded from 248.125) to fund their Washington trip.

The members would have to wash 117 cars (116.875) to fund their Valentine's Day Dance.

5. They would have to wash 366 cars.

Realistic

This can be realistic if there are a lot of members in the Math Club and if they set up in a good location. It will be successful.

Not Realistic

This is not realistic because there are many other factors that need to be taken into consideration. There might not be enough cars or people that are willing to get their car cleaned by these students. There are other supplies that they might need to buy and more.