wife gets 3/8
son gets 1/2 * 5/8 = 5/16
daughters each get 1/5 (1 - 3/8 - 5/16) = 1/16
son gets 1/2 * 5/8 = 5/16
daughters each get 1/5 (1 - 3/8 - 5/16) = 1/16
1. The man left thirty-eight of his money to his wife.
2. This means the wife received 38 units out of the total money.
3. The man had the remainder of the money after giving 38 units to his wife.
4. He then gave half of the remainder to his son.
5. This means the son received 1/2 * (total money - 38) units.
6. The rest of the money (total money - 38 - son's share) was divided equally among five daughters.
7. Each daughter received (total money - 38 - son's share) / 5 units.
To find the fraction of money each daughter received, we need to express each daughter's share as a fraction of the total money.
Let's perform the calculations:
- Daughter's Share = (total money - 38 - son's share) / 5
- = (total money - 38 - (1/2 * (total money - 38))) / 5
- = (total money - 38 - (1/2 * total money - 1/2 * 38)) / 5
- = (total money - 38 - (1/2 * total money - 19)) / 5
- = (total money - 38 - 1/2 * total money + 19) / 5
- = (total money - 1/2 * total money - 38 + 19) / 5
- = (1/2 * total money - 19) / 5
Therefore, each daughter received (1/2 * total money - 19) / 5 fraction of the total money.
Step 1: Calculate the amount of money left after leaving 38 units to the wife.
Let's assume the man had x units of money. Then, after leaving 38 units to his wife, he would have (x - 38) units of money remaining.
Step 2: Calculate half of the remaining money left for the son.
Half of the remaining money is (1/2) * (x - 38) units.
Step 3: Calculate the money left to be divided among the five daughters.
The money left to be divided among the five daughters is the remaining money after giving half to the son. So, it would be (x - 38) - (1/2) * (x - 38) units.
Step 4: Divide the remaining money equally among the five daughters.
To find the fraction of money each daughter received, we need to divide the amount left for the daughters by 5 (the number of daughters).
So, the fraction each daughter received is:
[(x - 38) - (1/2) * (x - 38)] / 5 units.
Simplifying the expression:
[(x - 38) - (1/2) * (x - 38)] / 5 = [(2x - 76 - x + 38) / 2] / 5
= (x - 38) / 10
Therefore, each daughter received (x - 38) / 10 fraction of the total money.