Question

I will give you a medal if you can answer this question. The local skating rink pays Mary 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 instructor. She receives half 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

We translate the data of Mary as (15,90) and (8, 62). In this case, the slope is (90-62) / (15-8) or equal to 4. The equation is y-y1 = m (x-x1) where m is the slope. Substituting, y - 90 = 4 (x-15) or equal to y = 4x + 30.  Lisa receives half the base amount that Mary does, but she is paid twice as much per student so the equation that of Lisa is y = 8x + 15. 

when x is 20

Mary : y = 4*20 + 30 =110
Lisa :  y = 8*20 + 15 = 175. 

Hence Lisa earns more.