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?

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

$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.

Oh, calculating wills, huh? Talk about dividing the dough-liciousness! Let's dive into the math-tastic world of fractions, shall we?

First, let’s find out how much money the younger children received altogether. If each younger child got #108,000 and there are four of them, that means the total amount they received is 4 * #108,000 = #432,000.

Now, we need to find the remainder after the eldest child got 2/5 of it. If the remainder is #432,000, we multiply it by 5/3 because 2/5 is equivalent to multiplying by 5/2. So, #432,000 * 5/3 = #720,000.

Finally, we need to find out how much the man had in total. If 4/9 of his money went to his wife and we know that #720,000 is 5/9 of his money, we can multiply #720,000 by 9/5 to find out his total money. That gives us #720,000 * 9/5 = #1,296,000.

Now for the big reveal, drumroll, please... After all that math-juggling, the wife's share is 4/9 of #1,296,000. So, 4/9 * #1,296,000 = #576,000.

So, the lucky wife got a whopping #576,000! I hope she puts it to good use and maybe even treats herself to a clown comedy show! 🤡

Let's break down the problem step-by-step:

Step 1: Find the total amount of money left for the younger children.
Let X be the total money left for the younger children.
The total money left is divided equally among the four younger children, so each child receives X/4.

Step 2: Determine the value of X.
Since each of the four younger children receives #108,000, the total amount of money left for them is 4 * #108,000 = #432,000. Hence, X = #432,000.

Step 3: Calculate the remainder after the younger children's share.
The remainder is the money left after giving the younger children their share. Thus, the remainder is X = #432,000.

Step 4: Calculate the amount of money the eldest child receives.
The eldest child receives 2/5 of the remainder. Therefore, the eldest child's share is (2/5) * #432,000 = #172,800.

Step 5: Calculate the remaining amount left for the wife.
The remaining amount left for the wife is the remainder after giving the eldest child their share. Thus, the wife's share is #432,000 - #172,800 = #259,200.

Therefore, the wife's share is #259,200.

To find the wife's share, we need to work through the problem step by step. Let's start by assigning variables to the given information.

Let's say the man's total money is represented by 'M'.

According to the will, the man left 4/9 of his money to his wife. Since 4/9 is the wife's share, we can calculate it as (4/9) * M.

The remaining money after the wife's share is deducted is represented by 'R'.

R = M - (4/9) * M

The will also states that the eldest child receives 2/5 of the remainder. So, the eldest child's share can be calculated as (2/5) * R.

The remaining amount after the eldest child's share is deducted is represented by 'C'.

C = R - (2/5) * R

Given that each of the four younger children receives #108,000, we can calculate their total share by multiplying this amount by the number of younger children: 4 * 108,000.

Since the four younger children share the rest equally, their total share is equal to the remaining amount, C.

Now we can set up an equation to solve for M:

C = 4 * 108,000
C = 432,000

Substituting the value of C, we can solve for R:

432,000 = R - (2/5) * R
432,000 = (1 - 2/5) * R
432,000 = (3/5) * R
R = (5/3) * 432,000
R = 720,000

Now, substituting the value of R, we can solve for M:

720,000 = M - (4/9) * M
720,000 = (1 - 4/9) * M
720,000 = (5/9) * M
M = (9/5) * 720,000
M = 1,296,000

Therefore, the man's total money, M, is #1,296,000.

Now, let's calculate the wife's share, which is (4/9) * M:

Wife's share = (4/9) * M
Wife's share = (4/9) * 1,296,000
Wife's share = 576,000

Therefore, the wife's share is #576,000.