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Will Wangle (Posted on 2014-02-13) Difficulty: 2 of 5
In his will Ethan left all his money to his children in the following manner:
  1. $1000 to the first born and one tenth of what then remains, then:
  2. $2000 to the second born and one tenth of what then remains, then:
  3. $3000 to the third born and one tenth of what then remains, and so on.....
When this is done each child had the same amount.
How many children were there?

No Solution Yet Submitted by K Sengupta    
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Solution Two-variable solution | Comment 3 of 5 |
I found the algebra a little easier with two variables.

Let p = each child's payment
     T = total inheritance
    
Then, for the first child,     p = 1000 + (T- 1000)/10
         for the second child, p = 2000 + (T - p - 2000)/10
      
Subtracting equation 1 from 2 gives
     0 = 1000 + (-p - 1000)/10
     p + 1000 = 10,000
     p = 9,000
     So T = 81,000

Number of children = 81,000/9,000 = 9 

Edited on February 14, 2014, 5:51 pm
  Posted by Steve Herman on 2014-02-13 15:37:21

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