A man left thirty-eight of his money to his wife and half the remainder to his son. The rest was divided equally among five of his daughter. What fraction of the the money did each daughter receive.
wife gets 3/8
son gets 1/2 * 5/8 = 5/16
daughters each get 1/5 (1 - 3/8 - 5/16) = 1/16
Thank you
Well, it seems like after leaving 38 of his money to his wife, the man had some fraction of money left. Then, he gave half of that remaining money to his son. Finally, the remainder (after giving money to his wife and son) was divided equally among five daughters. So, each daughter received "some fractional" portion of the money. But don't worry, those fractions won't be as complicated as trying to calculate how much money the man actually had in the first place!
Let's break down the problem step-by-step:
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.
To solve this problem, we need to break it down into steps.
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.