The ratio of Jims money to Peter's money was 4:7 at first. After Jim spent 1/2 of his money and peter spent $60, Peter had twice as much money as Jim. How much money did Jim have at first?
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.
j/p = 4/7
(j - j/2)/(p-60) = 1/2
(j/2)/(7j/4 - 60) = 1/2
4j = 7j-240
j = 80
Well, let's do some clown math, shall we?
If the ratio of Jim's money to Peter's money at first was 4:7, and Peter ends up with twice as much money as Jim, we can set it up like this: 4x and 7x.
Now, let's work through the problem step by step. If Jim spent half of his money, he'd be left with 4x/2, which simplifies to 2x.
Peter, on the other hand, spent $60 and ended up with twice as much money as Jim. So, we can say that 7x - 60 = 2(2x).
Now, let's solve for x. Distributing the 2, we get 7x - 60 = 4x.
Subtracting 4x from both sides, we have 3x - 60 = 0.
Adding 60 to both sides, we get 3x = 60.
Dividing both sides by 3, x = 20.
So, Jim's money at first would be 4x, which is 4 * 20 = $80.
And that, my friend, is the answer! Jim had $80 at first. Clown math for the win! 🤡
Let's assume that Jim had 4x dollars at first, where x represents the common ratio between their money.
According to the given ratio, Peter had 7x dollars at first.
After Jim spent 1/2 of his money, he was left with 4x - (1/2)(4x) = 4x - 2x = 2x dollars.
After Peter spent $60, he was left with 7x - 60 dollars.
According to the problem, Peter had twice as much money as Jim, so we have the equation:
2(2x) = 7x - 60
Simplifying the equation, we get:
4x = 7x - 60
Subtracting 7x from both sides, we have:
-3x = -60
Dividing both sides by -3, we get:
x = 20
So, Jim had 4x = 4(20) = 80 dollars at first.
To solve this problem, let's assign variables to represent the amounts of money Jim and Peter had at first.
Let's say Jim had '4x' dollars, and Peter had '7x' dollars.
According to the given information, after Jim spent half of his money, he had '4x - 0.5 * 4x' dollars left.
Peter, on the other hand, spent $60, so he had '7x - 60' dollars left.
We also know that at this point, Peter had twice as much money as Jim. Therefore, we can set up the equation:
7x - 60 = 2 * (4x - 0.5 * 4x)
Simplifying the equation, we get:
7x - 60 = 2(4x - 2x)
7x - 60 = 2 * 2x
7x - 60 = 4x
Next, we can subtract 4x from both sides of the equation to isolate the 'x' term:
7x - 4x - 60 = 0
3x - 60 = 0
Now, let's add 60 to both sides of the equation:
3x = 60
Finally, divide both sides by 3 to solve for 'x':
x = 60 / 3
x = 20
So, 'x' represents the common ratio between Jim and Peter's money. Since we know Jim had '4x' dollars at first, we can substitute 'x' with 20:
Jim had 4 * 20 = $<<4*20=80>>80 at first.