an estate valued at $62,000 is left by a will as follow:to each of two grandchildren a certain sum,to the son twice as much as to the two grandchildren together,and to the widow $2,000 more than to the son and granchildren together. How much goes to each?
one grandchild gets x
second grandchild gets x
son gets 4 x
widow gets 2,000 + 4 x + 2 x
so
2,000 + 4 x + 2x + 4 x + x + x = 62,000
12 x = 60,000
x = 5,000 to each grandkid etc etc etc
1st grandchild: $X.
2nd grandchild: $X.
Son: 2(x+x) = $4x.
Widow: X+X+4x+2000 = $(6x+2000).
x+x+4x + (6x+2000) = 62,000.
X = 5,000.
X = 5,000.
4x = 20,000.
6x + 2,000 = 32,000.
Let's break it down step by step:
Step 1: Let's assume the amount given to each grandchild is "x" dollars.
Since there are two grandchildren, the total amount given to them is 2x dollars.
Step 2: According to the will, the son receives twice as much as the two grandchildren combined.
So, the son receives 2 * (2x) = 4x dollars.
Step 3: The widow receives $2,000 more than the son and grandchildren combined.
Therefore, the widow receives (2x + 4x + $2,000) = 6x + $2,000.
Step 4: The total estate is valued at $62,000.
This means that the sums mentioned above must add up to $62,000.
Step 5: Now we can set up an equation to solve for the value of "x":
2x + 4x + 6x + $2,000 = $62,000
Step 6: Simplifying the left side of the equation:
12x + $2,000 = $62,000
Step 7: Subtracting $2,000 from both sides of the equation:
12x = $60,000
Step 8: Dividing both sides of the equation by 12:
x = $5,000
Step 9: Now, we can find the value for each person:
- Each grandchild receives $5,000.
- The son receives twice that amount, which is $10,000.
- The widow receives $2,000 more than the son and grandchildren combined, which is $12,000.
So, the amounts that go to each:
- Each grandchild: $5,000
- The son: $10,000
- The widow: $12,000
To solve this problem, we can break it down into three separate equations. Let's define the variables:
Let's call the amount going to each grandchild X.
Let's call the amount going to the son Y.
Let's call the amount going to the widow Z.
Now, let's form the equations using the given information:
1. Equation 1:
The sum of the amounts going to the two grandchildren is equal to the estate value.
2X + 2X = $62,000
2. Equation 2:
The amount going to the son is twice as much as the amount going to the two grandchildren together.
Y = 2(2X)
3. Equation 3:
The amount going to the widow is $2,000 more than the amount going to the son and grandchildren together.
Z = Y + 2X + $2,000
Now, we can solve this system of equations to find the values of X, Y, and Z.
From Equation 1:
4X = $62,000
Divide both sides by 4:
X = $15,500
Substituting the value of X into Equation 2:
Y = 2(2X)
Y = 2(2 * $15,500)
Y = $62,000
Substituting the values of X and Y into Equation 3:
Z = Y + 2X + $2,000
Z = $62,000 + 2($15,500) + $2,000
Z = $62,000 + $31,000 + $2,000
Z = $95,000
Therefore, the amounts that go to each beneficiary are as follows:
Each grandchild receives $15,500.
The son receives $62,000.
The widow receives $95,000.