logo for solving-math-problems.com
leftimage for solving-math-problems.com

Divide Estate - Word Problem - Algebra Alley

by danetra
(riverdale)










































An estate valued at $62,000 is left by a will as follows: to each of two granchildren a certain sum, to the son twice as much as the two grandchildren together, and to the widow $2000 more than to the son and grandchildren together. How much does each get?

Comments for Divide Estate - Word Problem - Algebra Alley

Click here to add your own comments

Mar 03, 2012
Divide Estate
by: Staff


Question:

by Danetra
(Riverdale)


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 the two grandchildren together, and to the widow $2000 more than to the son and grandchildren together. How much does each get?


Answer:

G = money left to each grandchild, separately

S = money left to son

W = money left to widow

2G + S + W = 62,000


to the son twice as much as the two grandchildren together

S = 2*2G


to the widow $2000 more than to the son and grandchildren together

W = 2G + S + 2000


You now have three equations and three unknowns


2G + S + W = 62,000


Substitute 2G + S + 2000 for W

2G + S + 2G + S + 2000 = 62,000


Substitute 2*2G for S

2G + 2*2G + 2G + 2*2G + 2000 = 62,000


Solve for G

2G + 2*2G + 2G + 2*2G + 2000 = 62,000

2G + 4G + 2G + 4G + 2000 = 62,000

12G + 2,000 = 62,000

12G + 2,000 - 2000 = 62,000 - 2,000

12G + 0 = 62,000 - 2,000

12G = 62,000 - 2,000

12G = 60,000

12G/12 = 60,000/12

G*(12/12) = 60,000/12

G*(1) = 60,000/12

G = 60,000/12

G = $5,000


Compute S

S = 2*2G

S = 4G

S = 4*$5,000

S = 4*$5,000

S = $20,000


Compute W

W = 2G + S + 2,000

W = 2*5,000 + 20,000 + 2,000

W = 32,000


>>>the final answer:

G = money left to each grandchild, separately = $5,000

S = money left to son = $20,000

W = money left to widow = $32,000


--------------------------------------------------
Check the answer by substituting the values of G, S, and W in the original equation:


2*5000 + 20000 + 32000 = 62,000

62,000 = 62,000, OK → G = 5000, S = 20000, and W = 32000 are VALID solutions



Thanks for writing.

Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com