SOLUTION: please help me solve this : a man left an amount of $525,000 to be divided among his widow, two sons and one daughter, each son was to receive twice the amount the daughter would r

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: please help me solve this : a man left an amount of $525,000 to be divided among his widow, two sons and one daughter, each son was to receive twice the amount the daughter would r      Log On


   

Question 697623: please help me solve this : a man left an amount of $525,000 to be divided among his widow, two sons and one daughter, each son was to receive twice the amount the daughter would receive, and the widow was to have eight times the amount each son would receive. how much was the widows share?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the share for 1 son
Let +d+ = the share for the daughter
Let +w+ = the share for the widow
given:
(1) +2s+%2B+d+%2B+w+=+525000+
(2) +s+=+2d+
(3) +w+=+8s+
-------------
(2) +d+=+s%2F2+
Substitute this into (1)
(1) +2s+%2B+s%2F2+%2B+w+=+525000+
and, also, substitute (3) into (1)
(1) +2s+%2B+s%2F2+%2B+8s+=+525000+
(1) +4s+%2B+s+%2B+16s+=+1050000+
(1) +21s+=+1050000+
(1) +s+=+50000+
and
+w+=+8s+
+w+=+400000+
The widow's share is $400,000
check:
(2) +d+=+s%2F2+
(2) +d+=+25000+
and
(1) +2s+%2B+d+%2B+w+=+525000+
(1) +2%2A50000+%2B+25000+%2B+400000+=+525000+
(1) +100000+%2B+425000+=+525000+
(1) +525000+=+525000+
OK