A man dies and leave his estate to his sons.
The estate is divided as follows:
1st son gets 100 crowns + 1/10 of remainder of estate.
2nd son gets 200 crowns + 1/10 of remainder of estate ...
(n)th son gets 100 × (n) crowns + 1/10 of the remainder
Each son receives same amount.
How many sons were there, what did each receive, and what was the estate?
Answer: 9 sons, 8100 crowns,
which we derive as follows:
Let Sn be the share of each son, and E be the entire estate.
S1 = 100 + (E - 100)/10
S2 = 200 + (E - S1 - 200)/10
S1 = S2
200 + (E - S1 - 200)/10 = 100 + (E - 100)/10
2000 + E - S1 - 200 = 1000 + E - 100
How handy: the E's cancel!
1800 - S1 = 900
S1 = 900
S1 = 100 + (E - 100)/10
(E - 100)/10 = 800
E - 100 = 8000
E = 8100
So each got 900/8100 = 1/9
9 Sons.
