Expert: Scott A Wilson - 3/19/2011

Question
Hello, there.

I recently started at a position that pays in salary form, at 50 hours a week, and I wanted to figure out how much I'm making per hour, and how much of that is (technically) overtime.

So, I make $24,000, which is $461.53 per week.

If I've done it right, I should be able to figure it out like so:

$461.53=(40*x)+(y*1.5)

I used to love algebra, but it seems 5 years of underexposure has left me to forget how to solve for two variables. Also, feel free to point out any error I may have already made!

Thanks so much!

Answer
There are normally 40 hours in a week, so 50 is 40 hours + 10 overtime hours.
Overtime is usually time and a half, or 1.5 times regular salary.

That can be written as $461.53 = 40*x + 10*1.5*x, where x is the hourly wage.
Since 10*1.5=15, and 40+15 = 55, that is the same as $461.53 = 55x.
Dividing both sides by 55 gives 8.391454545, which is a hair short of $8.40 / hour.

How did you arrive at the amount per week?
I arrived at it by taking (7/365)24,000 = $460.27 a week.
I also tried (7/366)24,000 = $459.01 a week for leap year.
I also tried (7/365.25)24,000 = $459.96 a week for the running average of days/year.

Another way of doing it is to say the years wage is roughly 2000 times the hourly wage.
This would give an hourly wage of $12, and since 1 weeks would be equivalant to 55 hours,
that would be $660 per week.

At any rate, none of these come out to $461.53, though my first way was closest.