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

Mary --
f = fixed rate per person
b = base amount

b + 15f = 90 --- multiply by -1
b + 8f = 62
-----------
-b - 15f = -90 (result of multiplying by -1)
b + 8f = 62
------------add
-7f = - 28
f = -28/-7
f = 4

b + 15f = 90
b + 15(4) = 90
b + 60 = 90
b = 90 - 60
b = 30

Mary earns $30 base pay and charges $4 per person

Lisa earns half base pay of Mary.....30/2 = 15
paid twice as much per student ... 4 x 2 = 8
so Lisa earns $15 base pay and charges $8 per person

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for 20 students...
Mary makes : b + 20h = total earned for 20 students
30 + 20(4) = 30 + 80 = 110
so Mary makes $110 for teaching 20 students

Lisa makes : b + 20(8) = total earned for 20 students
15 + 160 = 175
so Lisa makes $175 for teaching 20 students
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so who earns more ??