The question says:

A zoo charges $6 for adults, $3 for students, and $.50 for children. One morning 79 people enter and pay a total of $207. Determine the possible numbers of adults, students, and children.

So, I got the equations 6a+3s+0.5c = 207 and a+s+c=79. I then put them into a matrix and got it into REF that looks that

[ 1 0 0.83333 -10]

[ 0 1 1.83333 89]

I feel this should be really easy, but i cannot get a solution with guess and check.