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

The expressions for the payment made to Mary are,
         (Monday)      90 = 15m + b
         (Tuesday)     62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30. 
The equation that represents Mary's earning is 
                                    y = 4x + 30
 For 20 students,
                                    y = 4(20) + 30 = 110
For Lisa's earnings,
                                     y = 8x + 15
Substituting 20,
                                    y  =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.