A plant supervisor must apportion her 40-hour workweek between hours working on the assembly line and hours supervising the work of others. She is paid $12 per hour working and $15 per hour for supervising. If her earnings for a certain week are $504 how much time does she spend on each task?

Question

A plant supervisor must apportion her 40-hour workweek between hours working on the assembly line and hours supervising the work of others.  She is paid $12 per hour working and $15 per hour for supervising.  If her earnings for a certain week are $504 how much time does she spend on each task?

anonymous · Answer

Lets call the number of hours working 'w' and the number of hours supervising 's'.
From the question we know the total hours is 40:
$$w+s=40$$ 
We also know that total money earned is $540:
$$12w+15s=540$$
We can solve this by solving the first equation for w:
$$w=40-s$$
and substituting this into the second equation:
$$12(40-s)+15s=540$$$$480-12s+15s=540$$$$3s+480=540$$$$s=20 hours$$
We can now use our first equation to find that w=20.
She supervises for 20 hours and works for 20 hours.
We can check the answer with out equation:
$$12w+15s=540$$$$12(20)+15(20)=540$$$$540  =540$$

anonymous · Answer

Thanks man!

anonymous · Answer

Aaaaannnd I just realized I did the whole question with $540 and you said $504.......the steps are right though. 

This is why I shouldn't do math at 1:30 in the morning.

anonymous · Answer

Fixed for 504"

Same steps but you get 8 hours supervising ant 32 working. And the check works with the new numbers.