# Sari washes cars. She charges \$7 per minivan (m) and \$4 per car (c). She earned \$41 last weekend. How many vehicles of each type did she wash?

Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

Let's denote the number of minivans washed as m and the number of cars as c.

Then she earned 7m dollars for minivans and 4c for cars. It is given that

`7m+4c=41.`

If m and c could be negative and/or fractions, there would be many possible answers. But they cannot:)  m and c must be natural or zero each.

For this specific equation the simplest method is to check each possible value of, say, m.

4c=41-7m.

For m=0 4c=41 - impossible, 41 isn't divisible by 4.

For m=1 4c=41-7=34 - also impossible,

for m=2 4c=41-14=27,

for m=3 4c=41-21=20 - yes, it is possible,

for m=4 4c=41-28=13 - no,

for m=5 4c=41-35=6 - no.

m cannot be more than 5 because 4c must be nonnegative.

So there are only one possible answer, m=3 and c=20/4=5.

The answer: 3 minivans and 5 cars was washed.