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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.

Respuesta :

Lisa would earn $65 more than Mary.

Answer:

The correct option is :

Lisa would earn $65 more than Mary.

Step-by-step 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: [tex]15m+b=90[/tex]   .... (1)

For Tuesday: [tex]8m+b=62[/tex]     ....(2)

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

[tex]7m=28[/tex]

m = 4

[tex]15m+b=90[/tex]

[tex]15(4)+b=90[/tex]

[tex]60+b=90[/tex]

b = 30

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

[tex]y=4x+30[/tex]

For 20 students, the salary becomes:

[tex]y=4(20)+30[/tex]

[tex]y=80+30[/tex] = $110

Similarly, Lisa's earnings can be shown as :

[tex]y=8x+15[/tex]

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

[tex]y=8(20)+15[/tex]

[tex]y=160+15[/tex] = $175

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Now difference between both girl's salary = [tex]175-110=65[/tex] dollars.

So, the correct option is :

Lisa would earn $65 more than Mary.

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