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?

Lisa would earn $120 more than Mary.
Lisa would earn $65 more than Mary.
Mary would earn $15 more than Lisa.
Mary would earn $10 more than Lisa.

Answer 1

Lisa would earn $65 more than Mary.

Answer 2

The correct option is :

Lisa would earn $65 more than Mary.

Explanation:

Let 'b' define base salary of Mary.

Let 'm' define the fee per student.

As per given information, Mary's expressions become:

For Monday:
`15m+b=90` .... (1)

For Tuesday:
`8m+b=62` ....(2)

Subtracting (2) from (1) to get the value of m

`7m=28`

m = 4

`15m+b=90`

`15(4)+b=90`

`60+b=90`

b = 30

So, the complete equation that represents Mary's salary is :

`y=4x+30`

For 20 students, the salary becomes:

`y=4(20)+30`

`y=80+30` = $110

Similarly, Lisa's earnings can be shown as :

`y=8x+15`

So, for 20 students, Lisa's salary is :

`y=8(20)+15`

`y=160+15` = $175

-----------------------------------------------------------------------------------

Now difference between both girl's salary =
`175-110=65` dollars.

So, the correct option is :

Lisa would earn $65 more than Mary.