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
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.
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.