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
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
Let's start by calculating the amount of money James receives. We know that James gets $3.00.
Since Peter gets ⅔ of the total amount of money, this means that John and James share the remaining ⅓ of the money.
Let's assume the total amount of money shared is represented by the variable "x".
Peter's share = (⅔) * x
John and James share = (⅓) * x
Since John gets ¾ of the remaining share, we can write:
John's share = (¾) * (⅓) * x
Since we know James gets $3.00, we can set up the following equation:
John's share + James' share = $3.00
(¾) * (⅓) * x + $3.00 = $3.00
Simplifying the equation:
(9/12) * (1/3) * x + $3.00 = $3.00
(3/12) * x + $3.00 = $3.00
(1/4) * x = 0
To solve for x, we multiply both sides of the equation by 4:
x = 0 * 4
x = 0
Therefore, the total amount of money shared is $0.
To find the total amount of money shared, we need to work backwards from the given information.
Let's start with James, who received $3.00. This represents ¼ of the remaining amount after Peter received his share. So, we can calculate the remaining amount as follows:
Remaining amount = $3.00 / (3/4) = $3.00 * (4/3) = $4.00
Now, we know that Peter got ⅔ of the total amount. We can find Peter's share by multiplying the remaining amount by ⅔:
Peter's share = $4.00 * (2/3) = $8.00 / 3 = $2.67 (approx)
Finally, to find the total amount of money shared, we add up the amounts received by each person:
Total amount = Peter's share + John's share + James's share
Total amount = $2.67 + $4.00 + $3.00
Total amount = $9.67
Therefore, the total amount of money shared is approximately $9.67.
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