SOLUTION: 2 grandchildrenAn estate is to be distributed among a wife, three children, and two grandchildren. The children will recieve three times as much as each grandchild, and the wife wi

Algebra ->  Equations -> SOLUTION: 2 grandchildrenAn estate is to be distributed among a wife, three children, and two grandchildren. The children will recieve three times as much as each grandchild, and the wife wi      Log On


   

Question 84686: 2 grandchildrenAn estate is to be distributed among a wife, three children, and two grandchildren. The children will recieve three times as much as each grandchild, and the wife will recieve four times as much as each child. If the estate amounted to $115,000, how much will person recieve?
Found 2 solutions by tutor_paul, checkley75:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem of 3 equations and 3 unknowns. Any time you have at least as many equations as you have unknowns, you can solve the problem! The key is to develop the 3 equations.
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First, define some variables for yourself:
Let W = Wife
Let C = Child
Let G = Grandchild
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From the given information in the problem, you can write (in terms of money) the following equations for the relationships of who is getting what:
Each child gets 3 times what each grand child got, so you can write:
Equation #1: C=3G
The wife gets 4 times each child, so you can write:
Equation #2: W=4C
The total amount of the inheritance is expressed as:
Equation #3: W+3C+2G=115000
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So now you have your 3 equations and 3 unknowns. Use substitution to find the unknowns:
4C%2B3C%2B2G=115000
4C%2B3C%2B%282C%2F3%29=115000
%2821C%29%2F3%2B%282C%2F3%29=115000
C=15000 - Each child gets $15000
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G=C%2F3
G=15000%2F3
G=5000 - Each grandchild gets $5000
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W=4C
W=4%2A15000
W=60000 - The wife gets $60000
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Good Luck,
tutor_paul@yahoo.com

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
1 wife, 3 children & 2 grandchildren.
2G+3*3*G+4(3*G)=115000
2G+9G+12G=112000
23G=115000
G=115000/23
G=5000 FOR EACH GRANDCHILD.
3*5000=15000 FOR EACH CHILD
4*15000=60000 FOR THE WIFE.
PROOF
2*5000+3*15000+60000=115000
10000+45000+60000=115000
115000=115000