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? I tried by reading piece by piece and breaking it up but its gets more and more confusing...need help and understanding right away!!!:)
sorry! theres a modification:
the 2 grandchildren each gets x dollars.
son gets 2(2x) dollars
widow gets 2(2x)+2000+2x dollars
all add up to $62000
solve for x and then find out how much each person gets using by substituting x to the values..
To solve this problem, let's break it down step by step.
Step 1: Let's represent the amount given to each grandchild as 'x'. This means that each grandchild receives 'x' amount.
Step 2: According to the will, the son receives twice as much as the two grandchildren combined. So the son receives 2 * 'x'.
Step 3: The widow receives $2,000 more than the son and grandchildren together. So the widow receives (2 * 'x') + $2,000.
Step 4: The total value of the estate is $62,000. Therefore, the sum of the amounts given to each individual should add up to $62,000.
Now we can set up an equation to solve for 'x'.
'x' + 'x' + 2 * 'x' + (2 * 'x') + $2,000 = $62,000
Simplifying the equation:
6 * 'x' + $2,000 = $62,000
Subtracting $2,000 from both sides:
6 * 'x' = $60,000
Dividing both sides by 6:
'x' = $10,000
So each grandchild receives $10,000.
Now we can find the amounts received by the son and the widow:
Son: 2 * $10,000 = $20,000
Widow: (2 * $10,000) + $2,000 = $22,000
To summarize:
Each grandchild receives $10,000.
The son receives $20,000.
The widow receives $22,000.
the 2 grandchildren each gets x dollars.
son gets 2(2x) dollars
widow gets 2(2x)+2000 dollars
all add up to $62000