Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

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/   
    
Associated Topics:
High School Basic Algebra
High School Puzzles

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/