In his will Ethan left all his money to his children in the following manner:
- $1000 to the first born and one tenth of what then remains, then:
- $2000 to the second born and one tenth of what then remains, then:
- $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?
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
Two-variable solution
