SOLUTION: Please help me set up to solve this problem: A father left 1/2 of his estate to his son, 1/3 of his estate to his granddaughter, and the remaining $6000 to charity. What was his

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Question 163856This question is from textbook Mathematics in our World
: Please help me set up to solve this problem:
A father left 1/2 of his estate to his son, 1/3 of his estate to his granddaughter, and the remaining $6000 to charity. What was his total estate?
Thank you in advance!
Randi This question is from textbook Mathematics in our World

Found 2 solutions by kennedysj, ankor@dixie-net.com:
Answer by kennedysj(5) About Me  (Show Source):
You can put this solution on YOUR website!

Let x be the total amount of the estate.
Then %281%2F2%29%2Ax+= son's share
%281%2F3%29%2Ax = granddaughter's share
So %281%2F2%29%2Ax+%2B+%281%2F3%29%2Ax+%2B+6000+=+x or the total estate.
Solving this equation requires finding a common denominator of 6 for the fractions.
+%283%2F6%29%2Ax+%2B+%282%2F6%29%2Ax+%2B+6000+=+x
combining like terms we get
%285%2F6%29%2Ax+%2B+6000+=+x
Subtracting the (5/6)*x from both sides gives us
+6000+=+%281%2F6%29%2A+x
Multiplying both sides by 6 gives us
36000+=+x
Therefore the entire estate was $36000.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A father left 1/2 of his estate to his son, 1/3 of his estate to his granddaughter, and the remaining $6000 to charity. What was his total estate?
:
Let x = his total estate
:
total estate = son$ + daughter$ + $6000
x = 1%2F2x + 1%2F3x + 6000
Multiply equation by 6 to get rid of the denominators, solve for x