How Much Money?

Date: 08/16/2001 at 11:50:37
From: R.Jessica
Subject: Resolve this sum

Dear Dr. Math,

A man has 3 daughters, 4 sons, and a sum of money. If he divides the 
money equally among his daughters, $2 will be left over. If he divides 
the money among his sons, $2 will be also left over. If he divides the 
money equally among his daughters and sons, $1 will be left over. How 
much is the sum of the money if it is less than $100.00?

Thank you so much for your help.
R. Jessica

Date: 08/16/2001 at 14:32:39
From: Doctor Terrel
Subject: Re: Resolve this sum

Hello,

This is an example of a popular style of problem involving remainders 
after dividing by certain numbers. Perhaps the best way to solve 
this by non-algebraic methods is to examine some simple numerical 
cases.

I recommend that for this problem you first look at the case for sons 
and daughters combined: 7. What would be the smallest number of 
dollars that would leave $1 after dividing it among all the children?  
$8, right?  And look... it works for daughters, too. But it doesn't 
work for sons. We must try something else.

When we try $15 ($8 + $7), it only works for the children combined, 
not girls alone, or boys alone.

We should not give up yet. Just keep adding $7 to our last value ($22, 
$29, ...) and sooner or later we will find the answer. Remember, we 
were told the amount was less than $100.

This should help you find the answer.  If not, ask again please.

- Doctor Terrel, The Math Forum
  http://mathforum.org/dr.math/