A man made a will in which he left 4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children. If each of the younger children received #108,000; what was his wife's share?

Answer 1

T = Total money

If he left 4 / 9 of his money to his wife, wife's share is W = 4 T / 9

the remainder is R = T - W

R = 9 T / 9 - 4 T / 9

R = 5 T / 9

2 / 5 of the remainder to his oldest child is:

( 2 / 5 ) R = ( 2 / 5 ) * 5 T / 9 = 2 T / 9

The rest is:

T - W - 2 T / 9 = T - 4 T / 9 - 2 T / 9 = T - 6 T / 9 =

9 T / 9 - 6 T 9 = 3 T / 9 = 3 T / 3 * 3 = T / 3

The rest be shared with 4 equal parts.

( T / 3 ) / 4 = T / 12

Each of the younger children received 108,000

T / 12 = 108,000

T = 12 * 108,000 = 1,296,000‬

Total money = 1,296,000

Wife's share:

W = ( 4 / 9 ) * 1,296,000 = 576,000‬

Proof:

Remainder:

R = T - W = 1,296,000 - 576,000 = 720,000

2 / 5 of the remainder to his oldest child = ( 2 / 5 ) * 720,000 = 288,000‬

Rest = T - W - 288,000 = 1,296,000 - 576,000 - 288,000 = 432,000

432,000 be shared equally among his four younger children:

432,000 / 4 = 108,000

Answer 2

$X in will.
Wife received 4x/9.
Bal. = x - 4x/9 = 9x/9 - 4x/9 = 5x/9.
Oldest child received 2/5 * 5x/9 = 2x/9.
Bal. = 5x/9 - 2x/9 = 3x/9.

3x/9 = 4*108,000 = 432,000.
X = $1,296,000.

4x/9 = 4/9 * 1,296,000. = $576,000.