Peter ,John and James share a certain amount of money. Peter gets ⅔ of the money. John gets ¾ of the remainder and James gets $3 .calculate the total amount of money shared?
Peter gets 2/3, leaving 1/3
John gets 3/4 * 1/3 = 1/4, leaving 1/12
1/12 x = 3
now finish it off
8
Let's start solving the problem step-by-step.
Step 1: Let's assume the total amount of money shared is "x".
Step 2: According to the problem, Peter gets ⅔ of the money, which is equal to (2/3)x.
Step 3: Now we need to calculate the remainder. The remainder is the amount left after Peter receives his share. So the remainder is (1/3)x.
Step 4: John gets ¾ of the remainder, which is equal to (3/4) * (1/3)x = (1/4)x.
Step 5: After John receives his share, there is still a remainder of (3/4) * (1/3)x = (3/12)x left.
Step 6: According to the problem, James receives $3, which is equal to (3/12)x.
Step 7: Now we can determine the equation to find the value of x. The equation is (2/3)x + (1/4)x + (3/12)x = x.
Step 8: Let's solve the equation.
- Multiplying the whole equation by 12 to eliminate the fractions: 8x + 3x + 3x = 12x.
- Simplifying the equation: 14x = 12x.
- Subtracting 12x from both sides: 14x - 12x = 0.
- Simplifying the equation: 2x = 0.
- Dividing by 2 on both sides: 2x/2 = 0/2.
- Simplifying the equation: x = 0.
Step 9: Since x = 0, it means that there was no money shared because all the shares and remainder are 0.
Therefore, the total amount of money shared is $0.
To calculate the total amount of money shared, let's break down the information step by step:
1. Peter gets ⅔ of the money, which means the remaining share is ⅓ of the original amount.
2. John gets ¾ of the remainder, meaning he receives ¾ * ⅓ = ⅔ of the original amount. Since James gets $3, this must be the same amount.
3. Therefore, if ⅔ of the original amount equals $3, we can calculate the full original amount of money:
(1 / 3) * X = $3
Multiplying both sides by 3:
X = $3 * 3
X = $9
So, the total amount of money shared among Peter, John, and James is $9.