Question

Please help with linear equation! 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?

I will solve, I just need help

Answer 1

What I did:
m=(62-90) / (8-15)
y - 90= -4(x-15)
y=150-4x
y=(150-4(20) = 70

but thats not one of my answer choices

Answer 2

My choices:
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 3

Now, Mary first:
Let x is the money Mary can receive when tutoring 1pupil
a is the base amount
so, for Monday, her salary is 90 and 90 = a+ 15x, right?

Answer 4

for Friday, she received $62 with 8 students, so that 62 = a + 8x, right?
so far, you have 2 equations:
\[\begin {cases}90=a+15x\\62=a+8x\end{cases}\]
solve for a and x.

Answer 5

What do you have??

Answer 6

hailee you need to get your equations right

Answer 7

when you have a, which is base amount, you can know what the base amount Lisa received, because it is 1/2 a, right?
Moreover, you know x--> you will know how much Lisa received from 1 student, it is 2x, right?

Answer 8

Apply all to the equations of Mary and Lisa, you can compare the result to get the right answer.

Answer 9

Let Mary rate be r and base amount be x,
15r + x = 90 -(1)
8r + x = 62 -(2)

Solving, we have r = (18/7) and x = (360/7)

Since Lisa's rate is 2x and base amount is half of Mary's,
let Lisa's rate be 2r and base amount be (1/2)x.

Therefore, Lisa's rate = (36/7) and base amount = (360/14)

For 20 students, ....

You can continue from here

Answer 10

@OOOPS I got a=30 and x=4
So 15 is her base amount and 8 is per student of Lisa?