I need a formula for calculating overtime wages?

Question

I am attempting to comply with a wage law that requires I allocate bonus wages paid in a week in proportion to the regular and overtime hours paid during that same week. I will try to illustrate...

40.0 hours Regular Wages @ $10.00 per hour = $400.00
10.0 hours Overtime Wages @ $15.00 per hour = $150.00
40.0 hours Regular Bonus @ $??.?? per hour = $ ??.??
10.0 hours Overtime Bonus @ $??.?? per hour = $ ??.??
Total Wages = $650.00

The $100.00 bonus must be allocated across the 40.0 hours of regular time and the 10.0 hours of time-and-a-half overtime. What's the fastest way to calculate the regular and overtime rate for the bonus so they both total $100.00 and yet the bonus overtime rate is 1-1/2 times the bonus regular rate? Keep in mind that this calculation must be performed for all combinations of regular and overtime pay and any amount of bonus.

Answer 1

If you mean that the bonus is supposed to be allocated in the same proportion as the rest, and it's supposed to be $100 in total, then:

$400/($400 + $150) x $100 = $72.73 is regular bonus, and
$150/($400+ $150) x $100 = $27.27 is overtime bonus.

This ensures that the bonus is allocated in the same proportions as the money paid (rather than the hours worked).

This formula works in general:

regular/(regular + overtime) x total bonus = regular bonus
overtime/(regular + overtime) x total bonus = overtime bonus

Answer 2

If you could specify how the figure of $ 100 for the regular bonus plus overtime bonus was arrived at, a general formula could be worked out. For example, what is the bonus payment rate in relation to the regular wage rate? Please provide this information in general terms, so that one can give you the formula you are looking for.