# Thread: Piecewise function regarding wages: A job pays time and a half for overtime...

1. ## Piecewise function regarding wages: A job pays time and a half for overtime...

I'm a bit confused on some intermediate piecewise questions.

A job pays time and a half for overtime(anything worked over 40 per week). Your hourly rate is 16.00$per hour. I've found the first two, 16x if x is less than or equal to 40 and 640+24(x-40) if x > 40. How do I find out how many hours they have to work in order to receive$1,200 per week(besides guessing the hours and run it through a calculator).

And secondly, If he wants to make that amount, but limit his weekly hours to a maximum of 60 hours per week, and will need to ask for a raise to meet that, how much does he ask for? I don't understand what to use for an equation at that point.

2. You seem to have it right.

Wages: $16*40 +$16*1.5*(x-40) = $1,200 -- Can you solve for x? Remember, 'x' is the total hours (assuming it is greater than 40), not just the over-time hours. Resisting the urge to simplify, we can see a little more about the inner workings of the formulation... That$16 is the present wage. Substituting for that an expression that means some percentage greater should move you toward the solution to the second question.

Let's see what you can do with this additional information.

3. For the first answer, regarding how many hours would they have to work, i got 63.33, or 64 if we need to round up to whole hours. So they need to work a total of 64 hours to make sure they make the 1200 they wanted.

For the final answer, I still cant quite put it on paper. I get what you're saying, but I can't seem to write it, I want to write something like 16+16(Xpercentage), and but that doesn't seem to fit correctly. So then I thought maybe i could use 16x for the terms, but that doesn't help me either.

Any tips or hints on that? It seems you gave me a big one, but I just can't place it into a equation.

4. Originally Posted by Lunar
For the first answer … i got 63.33, or 64 if we need to round up to whole hours.
You need to round only if you were instructed to.

You have already rounded your decimal approximation of 63⅓ hours to the nearest hundreth hour. (Without rounding, 63⅓ hours can also be stated as 63 hours 20 minutes.)

For the [second] answer … I thought maybe i could use 16x for the terms …
If by terms you mean the hourly pay rate, you can.

In this case, 16 is the current hourly rate and x represents the factor (1+r), were r is the decimal form of the percent by which the current hourly rate increases (to become the new hourly rate).

For example, if the pay raise were 5%, then r = 0.05, and 16x is then 16(1+0.05) or \$16.80 per hour.

To write the equation, follow tkhunny's form.

There are 60 hours worked per week; that's 40 regular hours and 20 overtime hours.

16x is the new hourly rate for regular hours and 1.5(16x) is the new overtime rate.

5. I was overthinking this so much. Thank you guys for your help.

6. QUOTE=Lunar;420250]I was overthinking this so much …[/QUOTE]That also grows your brain! You're now better prepared, for the next time your brain gets exposed to similar stuff.