Dividing the Prize Money
Date: 05/24/2000 at 03:57:29 From: Mike Sawbridge Subject: A problem that my students and I can't solve Dear Dr. Math: The problem below was found at the NRICH site: http://nrich.maths.org/mathsf/journalf/may00/prob1.html We can't find a solution. It seems like a tough one. Help us please. Rollerball - Problem Last weekend Mrs. Shoe won a prize and she gave her winnings to her children in order. The first child received 100 pounds and one tenth of the remainder. The second child received 200 pounds and one tenth of the remainder. The third child received 300 pounds and one tenth of the remainder, and so on. After sharing out her winnings in this way she found that she had divided the money equally amongst all her children. How many children were there? Mike Sawbridge
Date: 05/24/2000 at 08:16:41 From: Doctor Jerry Subject: Re: A problem that my students and I can't solve Hi Mike, Let c1 be the amount the first child received; from the problem: c1 = 100 + (p-100)/10 also, c2 = 200 + (p-c1-200)/10 Equations could be written for other children, but this turns out not to be necessary. The reason is that we are also told that p/n = c1, p/n = c2, etc, where n is the number of children. If you write out p/n = c1 you'll find: (10-n)p = 900n Also, writing out p/n = c2 (and using c1 in the expression for c2) you'll find: (100-9n)p = 17100n If you solve these two equations in n and p you'll find n = 9 and p = 8100. Nice problem. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/
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