Problema Solution

members of a senior class held a car wash to raise funds for thier senior prom. they charged $3 to wash a car and $5 to wash a pick up truck or a sports utility vehicle. if they earned a total of $275 by washing a total of 75 vehicals,how many cars did they wash

Answer provided by our tutors

Let x be the number of cars washed and let y be the number of pick-up trucks and SUVs washed. These are our unknowns.

If we multiply the amount they charged to wash a car ($3) by the number of cars washed (this is "x") and add the amount they charged to wash a truck or SUV ($5) by the number of trucks and SUVs they washed (this is "y"), we get the total amount of money they made. Thus,

($3)(x) + ($5)(y) = $275

We know the total number of vehicles washed (the number of cars washed plus the number of trucks and SUVs washed) is 75, so we also have 

x + y = 75.

So we have a system of linear equations,

3x + 5y = 275

x + y = 75

Now all you need to do is solve this system. Multiply the second equation by -3 to get

3x + 5y = 275

-3x - 3y = -225

Add these together and we get

2y = 50, so y = 25.

Then since x + y =75, and y = 25, plugging in gives x + 25 = 75, so x = 50

x = 50, y= 25.

So there were 50 cars washed and 25 trucks or SUVs washed.