The drama club is having a car wash as a fundraiser. They wash cars for $5 each and trucks for $8 each. How many of each type of vehicle did they wash if they raised $199 by washing 32 vehicles?

Okay, let's start by defining our variables

`c=`number of cars

`t=`number of trucks

There are 32 vehicles in total, so:

`c+t=32`

`t=32-c`

Now, let's use the other piece of information given in the problem (the amount of money):

`5c+8t=199`

`5c+8(32-c)=199`

`5c+256-8c=199`

`256-199=8c-5c`

`3c=57`

`c=19`

There are 19 cars. Therefore, the number of trucks is:

`32-19=13` trucks

Let's check our answer:

`19+13=32` vehicles

`19*5+13*8=95+104=$199`

It looks like our answers are correct and make sense. Hope this helps!

Given -

Rate to wash one car `=$.5`
Rate to wash one truck `=$.8`
Total Amount collected `=$.199`
Number of vehicles `=32`

Let -
Number of cars be `=x`
Number of trucks `=y`

Based on the above pieces of information, we can form two equations

`x+y=32` --------------(1) Total cars and trucks washed
`5x+8y=199`--------------(2) Total amount collected

Solve the 1st equation for `y`

`y=32-x`

Substitute `y=32-x` in equation (2)

`5x+8(32-x)=199`

`5x+256-8x=199`

`5x-8x=199-256=-57`
`-3x=-57`

`x=(-57)/(-3)=19`

Substitute `x=19` in equation (1)

`19+y=32`
`y=32-19=3`

`y=3`

Number of cars `x=19`
Number of trucks `y=3`