System of Equations with graphing, word problem

[oats]

I'm trying to help my daughter with her homework, i used to know this stuff a long time ago, my memory is not so great now.
Here is the problem.

"Chloe is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $90. Chloe will be earning a base salary of $70 per month from the gym, plus an additional $5 for every class she teaches. If Chloe teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Chloe's expenses and earnings be?

Write a system of equations, graph them, and type the solution."

We think we've fgured out the X as either 5x = 90 or 5x + 70 = 90. Which will either be 18 or 4.
But how do we figure out the Y so we can plot it on the graph? that' what we're having problems with? Any advice would be greatly appreciated, thank you.

Father of a 9th grader.
This is not common core as her school doesn't teach it, not sure if that changes the answer in any way shape or form.

 

[Deleted member 4993]

I'm trying to help my daughter with her homework, i used to know this stuff a long time ago, my memory is not so great now.
Here is the problem.

"Chloe is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $90. Chloe will be earning a base salary of $70 per month from the gym, plus an additional $5 for every class she teaches. If Chloe teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Chloe's expenses and earnings be?

Write a system of equations, graph them, and type the solution."

We think we've fgured out the X as either 5x = 90 or 5x + 70 = 90. Which will either be 18 or 4.
But how do we figure out the Y so we can plot it on the graph? that' what we're having problems with? Any advice would be greatly appreciated, thank you.

Father of a 9th grader.
This is not common core as her school doesn't teach it, not sure if that changes the answer in any way shape or form.

You write:

5x = 90 or 5x + 70 = 90

What is 'x'?

Please define your variables.

 

[Steven G]

1st of all you can use any variables you like to use, personally I like to use the variable Harvey, but you must define YOUR variables. Think about this, you have a job and your boss ask you to solve this problem and you respond back a few minutes later saying x=17 (or some number). Do you think that is a good answer. I would have 2nd thought on why I hired that person. So let's start off teaching you daughter to define her variables.

Let x = the number of classes Chloe teaches
Let e = how much Chloe earns the 1st month including the $90 fee.

I hope that it is clear that Chloe earns e = $70 + 5x - 90 = 5x - 20. If it is not clear to your daughter then put in different values for x.
Now the problem clearly says to write a system of equations which I personally think is ridiculous. What do you think that 2nd equation should be? Hint: What information have I not used yet??

 

[oats]

1st of all you can use any variables you like to use, personally I like to use the variable Harvey, but you must define YOUR variables. Think about this, you have a job and your boss ask you to solve this problem and you respond back a few minutes later saying x=17 (or some number). Do you think that is a good answer. I would have 2nd thought on why I hired that person. So let's start off teaching you daughter to define her variables.

Let x = the number of classes Chloe teaches
Let e = how much Chloe earns the 1st month including the $90 fee.

I hope that it is clear that Chloe earns e = $70 + 5x - 90 = 5x - 20. If it is not clear to your daughter then put in different values for x.
Now the problem clearly says to write a system of equations which I personally think is ridiculous. What do you think that 2nd equation should be? Hint: What information have I not used yet??

Defining the variables appears to be part of my problem with helping her, when I read the problem at the end it asks how much is chloe's earning and expenses? I thought these were the two variables? Is that wrong? So is it asking to show separate earnings and expenses? I'm not sure where the 5x-20 came from? I put 5x = 90 , x being how many classes are needed to come up with the 90, if the wage was separate and 5x + 70 = 90 if the wage was included, but I didnt know if it was supposed to be included or not maybe im overthinking it? and i wasnt sure about the 2nd equation at all, you include the wage the price per class and how many classes so im not sure what you didnt include?

 

[Steven G]

The 5x - 20 came from 70 + 5x - 90. Do you know where 70 + 5x - 90 came from? 70 - 90 = -20.
I admit that I missed where it said How much will Chloe's expenses and earnings be?
Yes, you are correct that the variables should be for expenses and earnings.

So let y = earnings, x= # of classes that Chloe teaches and z = expenses

want y - z = 0
y = 70 + 5x
z=90

That is the system of equations which I came up with. Again, I do not like this problem at all. There is no reason to have a system of equations here.

I would solve it like this.
let x= # of classes which Chloe teaches.

Solve 70 + 5x = 90

x=4

expenses = $90 (given)
earnings = 90 (want)

 

[Steven G]

I see that you want to graph these equations. Since y-z=0 implies z=y you should graph y = 70 + 5x and y=90.