Question 7006
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.