# 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

 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