Weirdly Equally Split
Algebra
Level
4
A lawyer read the will of a man who had several children.
- The first-born first gets $1000, and then of what remains.
- The second-born then gets $2000, and then of what remains.
- The third-born then gets $3000, and then of what remains.
- So on and so forth.
If each child got the same amount of money, how many children are there?
The answer is 9.
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1 solution
Let the father leave $x behind.
1000 + (x - 1000)/10 = 2000 + (x - 1000 - 2000 - (x - 1000)/10)/10
(x - 1000) - (x - 3000 - (x - 1000)/10) = 10(2000 - 1000) = 10000
2000 + (x - 1000)/10 = 10000
x = 10(10000 - 2000) + 1000 = $81000
The amount of money for each child
= 1000 + (81000 - 1000)/10 = $9000
Number of children
= 81000/9000 = 9