Expert: Scott A Wilson - 10/17/2010

Question
You and your sister decide to combine your weekly overtime earnings to buy a birthday gift for your mother. Your overtime rate is $18 per hour and your sister's overtime rate is $24 per hour. The total amount earned for the gift was $288. If you worked two more hours of overtime than your sister, how many overtime hours did each of you work?

Please provide all work and explanation. Thanks.


Answer
If your sister worked x hours of overtime, that would be 24x.
Your total contributin would be 18(x+2) = 18x + 36.
The sum of the two is 24x + 18x + 36 = 42x + 36.
Take 42x + 36 = 288, subtract 36 from both sides, and then divide both sides by 42.  That will give x, which is how much your sister worked.  Add 2 to get the amount you worked.