the question is in the details?

Question

solve with algebra

some students were doing a a car wash for a fundraiser. $5 to wash a car and $7.50 to wash a van. at the end of the car wash they smudged the results with water. they had to figure out how to find how many cars and how many vans had been there and gotten washed. there were 33 vehicles and all and the total of the price was $197.50. so how many of each vehicle had come??

solve in algebra please.

THANKS SO MUCH IF YOUR DOING THIS!!!

Answer 1

Call x the number of cars they washed and y the number of vans.

Their total cash received was
197.5 = 5x + 7.5y
They knew that they washed 33 vehicles...
33 = x + y

Now solve the system of 2 equations 2 unknowns...
y = 33 - x
197.5 = 5x + 7.5(33 - x)
197.5 = 5x + 247.5 - 7.5x
2.5x = 50
x = 20
y = 33 - x
y = 13

They washed 20 cars and 13 vans.

Answer 2

First, we introduce variables for the number of cars and vans.

Let c = the number of cars washed, and
v = the number of vans washed.

Since there were 33 vehicles in total, it is safe to say that

c + v = 33

Now, we know that each car washed cost $5, and each van washed was $7.50. That means $5.00 times the number of cars washed is represented as 5c, and the vans washed is best represented as (7.5)v. Together, 5c and (7.5)v should total 197.50. That is,

5c + (7.5)v = 197.50

Therefore,

c + v = 33
5c + (7.5)v = 197.50

These are the systems of equations to solve for.

Since c + v = 33, we can derive c and get c = 33 - v.

Now, we can plug in this value of c in the second equation:

5c + (7.5)v = 197.50
5[33 - v] + (7.5)v = 197.50

Expanding the brackets, we get

165 - 5v + (7.5)v = 197.50

Grouping like terms,

165 + (2.5)v = 197.50

(2.5)v = 32.50

Therefore, v = 32.50 / 2.5 = 13

So the number of vans v = 13.
To solve for c, we just keep in mind that c = 33 - v, so c = 33 - 13 = 20.

Therefore, c = 20 and v = 13.
The number of cars that got washed is 20, and the number of vans washed is 13.

Answer 3

ok set it up like this
x+y=33 (over)
5x+7.5y=197.5
then use subsitution and solve for y.
you come out with y=13
plug that back in and solve for x
you come out with x=20
just pick whichever one u want x and y to be. (car wise)