Question

Julie is a math tutor. She charges each student $210 for the first 7 hours of tutoring and $20 for each additional hour.




When the number of hours (h) that Julie spends tutoring a student is greater than 7 (h > 7), the equation that gives the amount (A) that Julie earns in dollars is A = 210 + 20(h + 7) A = 210 + 20(h - 7) A = -210 + 20(h - 7) A = 210 + (h - 7)/20 . If Julie earns $410 tutoring one student, the total number of hours she spent tutoring the student is 38 19 17 12 .

Answer 1

Alright so first thing is first...we can agree that at h = 7 hours...we know she will have only made 210 dollars right?

Answer 2

yep

Answer 3

So lets look at equation choice 1 for a quick example

\[\large A = 210 + 20(h + 7)\]

We know that when h = 7....this will come out to just the 210...well if you plug in 7 for 'h' here...we will certainly not get that right?

So we need one that looks something like

\[\large A = 210 + (h - 7)\] right?

Answer 4

Im pretty sure yeah

Answer 5

Well just because since the 210 is always there...we want the second part to cancel out when h = 7...and in this type of equation it will

Answer 6

So...we know she makes 20 dollars per hour over that 7...so it makes sense that if she works 1 hour over...she will make 20 dollars more....or 2 hours makes 40 dollars more etc....so we know it will be 20 times the # of hours over 7 that she works

So we have

\[\large A = 210 + 20(h - 7)\]

Answer 7

This is pretty each to check too....

If she works 10 hours total....that is 3 over the 7 right? so that would be an extra 60 bucks...or 270 dollars earned total

Our equation we think it is:

\[\large A = 210 + 20(h - 7)\]

We know h = 10 so

\[\large A = 210 + 20(10 - 7)\]
\[\large A = 210 + 20(3)\]
\[\large A = 210 + 60\]
\[\large A = 270 \checkmark \]

Answer 8

Ahh okay so what about if Julie earns $410 whats the total hrs she worked?