Web Results For:The ratio of john's money to Peter's money was 4:7 at first. After john spent 1/2 of his money and Peter spent $60. Peter had twice as much money as john. How much money did john have at first?
let amount of John's money be 4x
let amount of Peters money be 7x
after transaction, John has 2x
Peter has 7x-60
7x-60 = 2(2x)
3x = 60
x = 20
John at first had $80 and Peter had $140
check:
John spent half his money , so he has $40 left
Peter spent $60, so he has $80 left
Does Peter have twice as much as John? YES!
Let peter have Jim have $4x. Then the given ratio means that Peter has $7x.
Since Jim spent half his money, he now has $2x dollars.
Peter spent $60 and thus now has $(7x-60).
The final ratio of Jim's money to Peter's money is therefore 2x : (7x-60). This is given as 1:2.
Now we just need to solve the proportion by cross-multiplying.
2x : (7x - 60) = 1 : 2
1*(7x - 60) = 2*2x
7x - 60 = 4x
3x = 60
x = 20. Therefore Jim originally had $4x = $80.
Step 1: Let's assume that John had x dollars at first.
Step 2: According to the given information, the ratio of John's money to Peter's money was 4:7 at first. This means that Peter had (7/4)x dollars at first.
Step 3: After John spent half of his money, he had (1/2)x dollars left.
Step 4: Peter spent $60, so he had (7/4)x - $60 dollars left.
Step 5: According to the problem, Peter had twice as much money as John after these expenses. Therefore, we have the equation: (7/4)x - $60 = 2((1/2)x)
Step 6: Solving the equation, we can simplify it as follows:
(7/4)x - $60 = x
7x - 240 = 4x
7x - 4x = 240
3x = 240
x = 80
Therefore, John had $80 at first.
To solve this problem, we'll first set up the equations based on the given information. Let's denote John's initial money as "x" and Peter's initial money as "y".
1. The ratio of John's money to Peter's money at first was 4:7. This can be written as x:y = 4:7.
2. After John spent 1/2 of his money, he would have x/2 remaining.
3. Peter spent $60 and had twice as much money as John after spending. So, Pater's money after spending can be expressed as y - 60, and it is twice the remaining money John has, so we can write the equation 2 * (x/2) = y - 60.
Now, we can solve these equations to find the value of x (John's initial money).
From equation 2, we have:
2 * (x/2) = y - 60
x = (y - 60)
Substituting this value of x into equation 1:
(y - 60):y = 4:7
Cross-multiplying:
7 * (y - 60) = 4 * y
Expanding and simplifying:
7y - 420 = 4y
Bringing like terms to one side:
7y - 4y = 420
3y = 420
Dividing both sides by 3:
y = 420 / 3
y = 140
So, Peter's initial money (y) was $140.
Substituting this value of y back into x = (y - 60):
x = (140 - 60)
x = 80
Therefore, John had $80 at first.