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/ |
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