Question

Read the following scenario and write two equations we could use to solve to find for the number of cars and trucks washed. Use the variables C for cars washed and T for trucks washed. (Hint: both equations should have T and C). SCENARIO: Western's eSports Team raised money for charity by organizing a car wash. They washed a total of 80 vehicles and raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.

Answer 1

Let:

C = Number of cars washed

T = Number of trucks washed

They washed a total of 80 vehicles, so:

`C+T=80`

They raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.​ so:

`5C+7T=486`

Let:

`\begin{gathered} C+T=80_{\text{ }}(1) \\ 5C+7T=486_{\text{ }}(2) \end{gathered}`

From (1) solve for T:

`T=80-C_{\text{ }}(3)`

Replace (3) into (2):

`\begin{gathered} 5C+7(80-C)=486 \\ 5C+560-7C=486 \\ -2C=486-560 \\ -2C=-74 \\ C=(-74)/(-2) \\ C=37 \end{gathered}`

Replace the value of C into (3):

`\begin{gathered} T=80-37 \\ T=43 \end{gathered}`

They washed 37 cars and 43 trucks