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### How Much Money?

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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.

- Doctor Terrel, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Division
Middle School Puzzles

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