Question

peter,john and james share a certain of money.peter gets ⅔ of the amount of money.John gets ¾ of the remainder and james gets $3.00 calculate the total amount of money shared

Answer 1

let the total be x

solve : (2/3)x + (3/4)(1/3)x + 3 = x
2x/3 + x/4 + 3 = x
suggestion: times 12

take it from there

Answer 2

Firstly let $x be the total amount they have shared.
PETER--» (2/3 of the amount)
=$2/3x
JAMES--» (3/4 of the remainder)
=3/4(x - 2/3x)
=$(3/4x - 1/2x)
JAMES--» $3.00

If we add their shares although they should give us the total amount ($x)

$PETER+$JOHN+ $JAMES=$x
2/3x + 3/4x - 1/2x + 3=x
Now we collect the like terms
2/3x + 3/4x - 1/2x - x = -3
At this point we add using 12 as the common denominator.
(8x + 9x - 6x - 12x)/12 = -3
[8x+9x-6x-12x=-x]

-x/12=-3
Multiply both sides by 12
12(-x/12) = -3x12
-x=-36
Divide both sides by a (-1)
x=$36.00


Proof
PETER--» 2/3X36=$24.00
JOHN--» 2/4 X (36-24)
2/4X12
$9.00
JAMES--» $3.00

$ PETER+ $JOHN + $ JAMES =$x
$24.00+ $9.00 + $3.00 =$ 36.00