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.