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 N108000 what was his wife's share?
Let X be the amount of money the man had.
His wife received 4/9 * X.
The remainder is X - 4/9 * X = 5/9 * X.
His eldest child received 2/5 * 5/9 * X = 2/9 * X.
The younger children received 5/9 * X - 2/9 * X = 3/9 * X.
Each of the younger children received 108000, so 3/9 * X = 108000.
X = 108000 * 9/3 = <<108000*9/3=324000>>324000.
The wife's share is 4/9 * 324000 = 4/9 * 324000 = <<4/9*324000=144000>>144000. Answer: \boxed{144000}.
To find out the wife's share, we need to work through the given information step by step.
Let's assign a variable to represent the total amount of money the man had. Let's call it "M."
According to the will, the man left 4/9 of his money to his wife. So, the wife's share can be calculated as (4/9) * M.
Next, the will states that the man left 2/5 of the remainder to his eldest child. To calculate this amount, we need to subtract the wife's share from the total money, M. The remainder can be represented as (M - (4/9) * M).
Hence, the eldest child's share is (2/5) * (M - (4/9) * M).
Now, we know that the remaining money, after giving the wife and eldest child their shares, is divided equally among the four younger children. We are given that each of the younger children received N108000. Multiplying the amount each younger child received by the total number of younger children (4), we get the remaining amount.
So, (amount each younger child received) * (number of younger children) = N108000 * 4.
Now, we can create an equation to represent the total amount of money:
M = (4/9) * M + (2/5) * (M - (4/9) * M) + (N108000 * 4).
We can solve this equation to find the value of M, which represents the total amount of money the man had.
Let's solve the equation step by step:
Expanding the equation:
M = (4/9)M + (2/5)(M - (4/9)M) + (N108000 * 4).
Simplifying:
M = (4/9)M + (2/5)(M - (4/9)M) + 432000.
Now, we can solve for M:
Multiply through the brackets:
M = (4/9)M + (2/5)M - (4/5)(4/9)M + 432000.
Combine like terms:
M = (4/9)M + (2/5)M - (16/45)M + 432000.
Finding a common denominator for the fractions:
M = (20/45)M + (18/45)M - (16/45)M + 432000.
Combining like terms:
M = (22/45)M + 432000.
Now, we can isolate M by subtracting (22/45)M from both sides:
M - (22/45)M = 432000.
Simplifying:
(45/45)M - (22/45)M = 432000.
Combining like terms:
(23/45)M = 432000.
To find M, we can multiply both sides of the equation by (45/23):
(23/45)M * (45/23) = 432000 * (45/23).
Simplifying:
M = (20700/23) * 45.
Evaluating the right-hand side:
M ≈ 189,130.43.
Now that we know the total amount of money the man had, we can calculate the wife's share.
Wife's share = (4/9) * M.
Substituting the value of M:
Wife's share ≈ (4/9) * 189,130.43.
Calculating the wife's share:
Wife's share ≈ 84,170.10.
Therefore, the wife's share is approximately N84,170.10.
Let's solve this step-by-step:
Step 1: Determine the portion of money left for the wife.
The man left 4/9 of his money to his wife.
Let's assign the total amount of money as "M."
The amount left for the wife is (4/9) * M.
Step 2: Calculate the remainder after the wife's share.
The remainder after the wife's share is (1 - 4/9) * M = (5/9) * M.
Step 3: Determine the portion of money left for the eldest child.
The man left 2/5 of the remainder to his eldest child.
The amount left for the eldest child is (2/5) * [(5/9) * M] = (2/9) * M.
Step 4: Determine the remaining money after the wife's and eldest child's shares.
The remaining money after the wife's and eldest child's shares is [(5/9) * M] - [(2/9) * M] = (3/9) * M = (1/3) * M.
Step 5: Divide the remaining money among the four younger children.
The remaining money is to be shared equally among the four younger children.
Each younger child receives (1/4) * [(1/3) * M] = (1/12) * M.
Step 6: Calculate each child's share.
Since each of the four younger children received N108,000,
(1/12) * M = N108,000.
Therefore, M = N108,000 * 12 = N1,296,000.
Step 7: Determine the wife's share.
We know that the wife's share is (4/9) * M.
Substituting M = N1,296,000,
Wife's share = (4/9) * N1,296,000 = N576,000.
Therefore, the wife's share is N576,000.