Grade 10 students washed 53 vehicles and raised $382. They charged $6/car and $8/van. How many of each type of vehicle did the students wash?

Answer 1

You can solve this problem by creating two equations with two unknowns and solving them.

Let's use the variable, c, to represent the NUMBER of cars and the variable, v, to represent the NUMBER of vans.

Since there are a total of 53 vehicles, we can write the following equation:

c + v = 53

Then since each car was $6 and each van was $8 with a total of $382 raised, we can write the following equation:

6c + 8v = 382

Now solve these two equations using elimination. Multiply the first equation by -6 and solve for v:

-6c - 6v = -318

6c + 8v = 382

2v = 64

v = 32

There were 32 vans.

Since there were a total of 53 vehicles, there will be 21 cars (32 + 21 = 53)

To verify, the total amount raised would be $382:

6c + 8v = 382

6*21 + 8*32 = 126 + 256= 382