Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week.
Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours.
Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work?
someone help me!!

- anonymous

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- theEric

Hello! So, do you understand the first part?
"Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week."

- anonymous

yes theEric

- theEric

Okay! And then do you understand that we want to find a function \(S\) to say how much money was earned total, given \(y\) hours of overtime?

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## More answers

- anonymous

I get that part to.... I'm having trouble of finding S and Y

- theEric

Okay! Well, maybe we should actually think about that part! See, the goal, as it is written, is this:
"Create an equation that shows the amount of wages earned, S, for working y hours of overtime"
But let's pick out the important parts.
Create an equation [with] the amount of wages earned, S, [and] the hours of overtime, y.
We won't have any values, right away. We'll have a relationship between S and y. We can plug numbers in later.
And I shouldn't have said that it's a function :P

- theEric

So, since we have a variable for overtime hours, y, we have to think about overtime.

- theEric

If we have overtime hours, do we also have regular hours? The answer is yes. How many regular hours do we have, before we get more \(\it{overtime}\) hours?

- anonymous

it really does not say all that is says is that you work 40 hours a week and any hours over that is overtime

- theEric

Right! So, you have at least 40 hours of regular hours.
Now we'll look at this situation, and I see where the problem is being dumb and probably got you thinking. For this problem, we are (I think) supposed to ASSUME that we have at least forty hours. Then we wonder about only how many MORE hours.
Is that okay with you?

- theEric

The problem should say that... The answer is more complex if we have to consider any number of hours. We would have to have a couple possible cases: one from 0-40 hours, and one from 40 to infinity. But here, let's just worry about that last case.

- anonymous

yes that's ok with me.....

- theEric

Okay! So let's look at the total hours and their types.
How many regular hours do we have?
How many overtime hours do we have?
You tell me! (Hint: you can use "y" as an answer!)

- anonymous

regular hours we have 40 and over time we have y

- theEric

Right!
Now, we want to know about the money, so lets use the knowledge of how many hours we have, and turn that into money.
We get $6 for regular hours, and we have 40 regular hours. How much money is that?
We get $9 for overtime hours, and we have \(y\) regular hours. How much money is that?

- anonymous

now would we multiply 40 by 6

- theEric

Right! So, \(40\text{hours}\times 6\dfrac{\text{\$}}{\text{hour}}=\$240\).
That is baseline, then. We can get more, with overtime hours (y).
So, if we have y overtime hours, at $9/hour, how much money is that? It's very similar to regular hours, but we have a variable, y, instead of a number, like 40.

- anonymous

I'm a little confused

- theEric

Okay! That's because of the variable, probably! Working with numbers makes sense. But a variable is harder to work with. It could be any number! So we just have to think of what kind of quantity it is.
Our \(y\) is a number of hours. For each \(y\), we get $9, because \(y\) is overtime hours.
Sometimes you want to think about what \(y\) represents. If \(y\) was \(4\) hours, and we got $9/hour, how much would we get for just that overtime? It would be \(4\times 9 = $36\). What if \(y=5\)? Then \(5\times 9=$45\). And what if \(y=6\)? Then \(6\times 9=$54\). Now, if we don't really know, then we just put \(y\) where we need it. So, if we have jsut that, it's like \(y=y\), and we have \(y\times 9=$$$\).
We don't know how much money, because we don't know how many hours. But we do have a relationship between the two. Do you get that? You'll see that a lot, so it's worth looking at :)

- anonymous

Its starting to make a little more scene

- theEric

Good! It will DEFINITELY take time. Variables are tricky at first. But then they're useful. I remember when my brother first showed me his algebra. I had NO idea how letters could possibly have any use in math. But, I learned, they hold the spot for numbers that we \(\it {don't\ know\ about}\).

- theEric

Let's move on, just so you can see this problem play out. It won't make perfect sense, maybe. But seeing this through might help you understand the next problem you get. Is that okay?

- anonymous

@theEric you are very nice!

- anonymous

yes that's ok

- theEric

Haha, thank you, @xooj !

- theEric

Okay @Cgsmith ,
So, for the overtime hours, we'll get \(y\times 9\) dollars. And you figured out that, because we have 40 regular hours, we'll have \(40\times 6=240\) dollars.
Now we need to find "the amount of wages earned," which is just how the problem asks for the total amount of money from both types of hours. It's good to know that, for this problem, it calls the total money \(S\). It's a variable, too, because we don't know the number. We just know that it's the total amount of money.
Since we get \(y\times 9\) dollars AND $240, we have \(y\times 9 +240\) dollars. Is that okay? Now, if that's our total money, it's called \(S\)! So, we can say that \[S=y\times 9+240\]People often like to prefer to write multiplication with a variable with NO symbol, like this:\[S=9y+240\]
Is there anything you'd like me to clear up, there? Or do you just want to finish this up?

- anonymous

Nope its all clear to me now thanks for helping me bud @theEric

- theEric

Not a problem!! I'm glad I could help. So, that's part B.
Did you want me to go through C?

- anonymous

nah I got part c but thanks for asking anyways

- theEric

Awesome! Congrats, and take care!

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