Question

The local skating rink pays marry a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for instructing 15 students on Monday afternoon. last Friday, she earned $62 for working with 8 students. Lisa is also a skating intructor. She receives half of the base amount that Mary does, but she is paid twice as much per student. Who would earn more money instructing a class of 20 students?

Answer 1

You have to make a system of equations: lets make a equal the amount marry makes per student and b be her base amount.
90=15a+b (you have to subtract the top equation by the bottom equation)
62=8a+b   (90-62=28, 15a-8a=7a, and b-b=0)
Since b canceled out, you are left with 7a=28 which means a=4.  you can than plug a into the equation 62=8a+b to find that b=30.

since Lisa makes half of the base amount marry, her base amount is 15.  However, she also make twice the amount per kid so she makes 8 per kid.
using the found values found you can make the equations (m=the amount Marry makes, l=the amount Lisa makes, and c is the number of children)
m=4c+30
l=8c+15
set c=20 and you should get m=110 and l=175.  Based off of that information, we can say that Lisa makes more money instructing a class of 20 students.
I hope this helps.