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Question 7006: A man died and left the following instructions for his fortune
Half went to his wife
1/7 of what was left went to his son
2/3 of what was left went to his butler
the man's pet pig got the remaning $2000
How much money did the man leave behind altogether?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the deceased man's fortune.
To his wife, he leaves (1/2)x
To his son, he leaves (1/7) of (1/2)x
To his butler, he leaves (2/3) of ((1/7) of (1/2)x)
To his pig, he leaves the remaining $2,000.00
All these amounts should add up to $x, the deceased man's fortune.
(1/2)x + (1/7)(1/2)x + (2/3)(1/7)(1/2)x + $2,000.00 = $x Simplify and solve for x. Factor an x from the first three terms.
x(1/2 + 1/14 + 2/42) + $2,000.00 = $x Add up the fractions. The common denominator is 42.
x(21/42 + 3/42 + 2/42) + $2,000.00 = $x
x(26/42) + $2,000.00 = $x Simplify the fraction.
x(13/21) + $2,000.00 = $x Subtract x(13/21) from both sides.
$2,000.00 = $x - x(13/21)
$2,000.00 = $x(8/21) Multiply both sides by the multiplicative inverse of 8/21
$2,000.00(21/8) = $x
$x = $5,250.00 The deceased man's fortune.
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