SEARCH HOME
Math CentralQuandaries & Queries

search

Question from Maci, a parent:

We recently hosted a funraiser. Not everyone will receive a whole share of the profits because they did not participate the entire time. Several will receive only 1/2 or 1/3 share. How do I divide the profits?

Hi Maci.

First, allocate the shares in a way that seems appropriate. Here's my example:

Total profits: $400

Andrew: 1 share
Bev: 1/2 share
Cosmo: 2 shares
Dharma: 1/3 share
Eli: 2/3 share

Then add all the allocations together as fractions (find a common denominator):

1 + 1/2 + 2 + 1/3 + 1/3 = 6/6 + 3/6 + 12/6 + 2/6 + 4/6 = 27/6.

Now divide the total profits by this value (to divide by a fraction, we can multiply by the reciprocal) to find the value of each full share:

400 x ( 6/27 ) = $88.89 per share.

Now give people their own allocations (I'm doing a bit of rounding on the cents):

Andrew: 1 share = 1 x $88.89 = $88.89
Bev: 1/2 share = 1/2 x $88.89 = $44.44
Cosmo: 2 shares = 2 x $88.89 = $177.78
Dharma: 1/3 share = 1/3 x $88.89 = $29.63
Eli: 2/3 share = 2/3 x $88.89 = $59.26.

To check this, you add up those allocations. The total (within the rounding) should match the total profit from before:

$88.89 + $44.44 + $177.78 + $29.63 + $59.26 = $400.

Hope this helps,
Stephen La Rocque

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS