Question

An estate valued at 62,000 is left by a will as follows: 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 grandchildren together. How much goes to each?. grandchildren: #1 #2 Son: Widow: total $62,000.

what is the answer ​

Answer 1

Explanation:

The sum left to the two grandchildren is equal to a certain sum: G1 + G2.

The sum left to the son is twice as much as the sum left to the two grandchildren together: S = 2(G1 + G2).

The sum left to the widow is 2,000 more than the sum left to the son and the two grandchildren together: W = S + G1 + G2 + 2,000.

We also know that the total estate is valued at $62,000:

G1 + G2 + S + W = 62,000.

The sum left to the two grandchildren is equal to a certain sum: G1 + G2.

The sum left to the son is twice as much as the sum left to the two grandchildren together: S = 2(G1 + G2).

The sum left to the widow is 2,000 more than the sum left to the son and the two grandchildren together: W = S + G1 + G2 + 2,000.

We also know that the total estate is valued at $62,000:

G1 + G2 + S + W = 62,000.

G1 + G2 + 2(X) + (2(X) + X + 2,000) = 62,000.

G1 + G2 + 2X + 2X + X + 2,000 = 62,000

4X + G1 + G2 + 2,000 = 62,000.

4X + G1 + G2 = 60,000.

We have three equations now:

G1 + G2 = X.

S = 2X.

4X + G1 + G2 = 60,000.

From Equation 2, we have S = 2X, so X = S / 2.

G1 + G2 = S / 2.

2(G1 + G2) = S.

4X + (2(G1 + G2)) = 60,000.

2(2X) + 2G1 + 2G2 = 60,000.

4X + 2G1 + 2G2 = 60,000.

4X + G1 + G2 = 4X + 2G1 + 2G2.

G1 + G2 = 2G1 + 2G2.

G1 + G2 - 2G1 - 2G2 = 0.

-G1 - G2 = 0.

So, G1 = G2 = Y.

Now, from Equation 1, we know:

G1 + G2 = X.

But we just found that G1 = G2 = Y. So:

Y + Y = X.

2Y = X.

Now, we know that S = 2X, so:

S = 2(2Y).

S = 4Y.

Now, from Equation 3, we can find W:

W = S + X + 2,000.

W = 4Y + 2Y + 2,000.

W = 6Y + 2,000.

Now, we know that the total estate is $62,000:

G1 + G2 + S + W = 62,000.

But we found that G1 = G2 = Y and S = 4Y and W = 6Y + 2,000, so:

Y + Y + 4Y + (6Y + 2,000) = 62,000.

Combine like terms:

12Y + 2,000 = 62,000.

Now, subtract 2,000 from both sides:

12Y = 60,000.

Now, divide by 12 to find the value of Y:

Y = 60,000 / 12.

Y = 5,000.

So, each grandchild receives $5,000, the son receives 4 times that amount, which is $20,000, and the widow receives 6 times that amount plus $2,000, which is $32,000.

To summarize:

Each grandchild receives $5,000.

The son receives $20,000.

The widow receives $32,000.