a man left 1\2 of his estate to his wife, 1\6 to his daughter, and the remainder an amount of $15,000, to his son. How large was the entire estate?
To find out how large the entire estate was, we need to solve the equation using the given information.
Let's assume that the entire estate is represented by the variable "x".
According to the given information, the man left 1/2 of his estate to his wife, which would be (1/2) * x.
He also left 1/6 of his estate to his daughter, which would be (1/6) * x.
Lastly, he left the remainder, which is $15,000, to his son.
We can now represent this equation:
(1/2) * x + (1/6) * x + $15,000 = x
To solve this equation, we need to combine the like terms:
(3/6) * x + (1/6) * x + $15,000 = x
(4/6) * x + $15,000 = x
We can eliminate the fraction by multiplying both sides of the equation by 6:
6 * ((4/6) * x + $15,000) = 6 * x
(4/6) * 6 * x + 6 * $15,000 = 6 * x
4x + $90,000 = 6x
Now, subtract 4x from both sides of the equation:
4x - 4x + $90,000 = 6x - 4x
$90,000 = 2x
To isolate the variable x, divide both sides of the equation by 2:
$90,000/2 = 2x/2
$45,000 = x
Therefore, the entire estate was $45,000.
To determine the size of the entire estate, we need to calculate the sum of the amounts left to the wife, daughter, and son.
Let's start with the wife's share, which is 1/2 of the estate.
Next, we'll calculate the daughter's share, which is 1/6 of the estate.
Finally, we'll determine the son's share, which is $15,000.
To find the total size of the estate, we need to add up these three amounts:
Wife's share: 1/2 of the estate
Daughter's share: 1/6 of the estate
Son's share: $15,000
To calculate the size of the entire estate, we'll express the fractions as a common denominator:
Wife's share: (1/2) x (6/6) = 6/12
Daughter's share: (1/6) x (12/12) = 2/12
Now, we can add up the three parts:
Wife's share + Daughter's share + Son's share = 6/12 + 2/12 + $15,000
Adding the fractions: (6 + 2)/12 = 8/12 = 2/3
Therefore, the son's share of $15,000 represents 2/3 of the estate.
To find the size of the entire estate, we can set up a proportion:
(2/3) / ($15,000) = (1/1) / (x)
Cross-multiplying, we get:
2/3 * x = $15,000
To isolate "x," we can multiply both sides by 3/2:
(2/3 * x) * (3/2) = $15,000 * (3/2)
Simplifying:
2x = $22,500
Finally, dividing both sides by 2:
x = $11,250
Therefore, the size of the entire estate is $11,250.
entire estate value ---- x
x - (x/2 + x/6) = 15000
times 6
6x - 3x - x = 90000
2x = 90000
x = 45000
check
wife gets 22500
daughter gets 45000/6 = 7500
leaving 15000 for son
all adds up nicely.