A man left his property to his wife, his son, his daughter, and his sister. His son and daughter got half of the property, sharing in the ratio of 4 to 3. His wife got twice as much as the daughter. If his sister received $15,000, what was the value of all of his property?
Son and daughter got half, in the ratio of 4 to three.
So
son+daughter = 1/2
son got 4/14
daughter got 3/14
Wife got twice as the daughter = 6/14
Sister got 1-(4/14+3/14+6/14) = 1/14
If 1/14 of the property was worth $15,000, the value of his estate is
$15,000/(1/14) =?
Daughter's share = x-dollars.
Wife's share = 2x-dollars.
Son's share = 4x/3-dollars.
Sister's share = 15000 dollars.
The son and daughter received 1/2 of
the property. The other 1/2 went to the
wife and sister:
x + 4x/3 = V/2 = 2x + 15000,
x + 4x/3 = 2x + 15000,
Solve for x:
x = 45000 = Daughter's share,
2x = 2 * 45000 = 90000 = Wife's share,
4x/3 = 4*45000/3 = 60000 = son's share
V/2 = 2 * 45000 + 15000 = 105000,
V = 210000 = Value of property.
To find the value of all the man's property, we need to find the total value of the son and daughter's share, the wife's share, and the sister's share.
Let's start by determining the value of the son and daughter's share. We are told that they split half of the property, sharing in a ratio of 4 to 3. This means that the son's share is 4 parts out of 7 (4/7) and the daughter's share is 3 parts out of 7 (3/7).
Let's assume the total value of the property is x dollars.
The son's share will be (4/7) * x.
The daughter's share will be (3/7) * x.
Now, we know that the wife got twice as much as the daughter. So, the wife's share is 2 times the daughter's share, which is 2 * (3/7) * x = (6/7) * x.
Given that the sister received $15,000, we can set up the equation:
(4/7)x + (3/7)x + (6/7)x + $15,000 = x
Combine the x terms:
(13/7)x + $15,000 = x
Subtract (13/7)x from both sides:
$15,000 = (7/7)x - (13/7)x
Simplify:
$15,000 = (7 - 13)/7x
$15,000 = (-6/7)x
Multiply both sides by -7/6 to isolate x:
$15,000 * (-7/6) = x
Solve for x:
-$17,500 = x
Therefore, the value of all the man's property is $17,500.