The ratio of Jim’s money to Peter’s money was 4 : 7 at first. After
Jim spent half 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.
Peter & James had the same amount of money. After Peter spend $14.60 and James spend $8.20, James had twice as much money as Peter, how much money had each of them have at first?
To solve this problem, let's assume that both Peter and James initially had x amount of money.
After Peter spent $14.60, he would have x - 14.60 dollars left.
Similarly, after James spent $8.20, he would have x - 8.20 dollars left.
According to the given information, James had twice as much money as Peter after their expenses. Mathematically, we can express this as:
x - 8.20 = 2(x - 14.60)
Now, let's solve this equation to find the value of x:
x - 8.20 = 2x - 29.20
Subtracting x from both sides:
-8.20 = x - 29.20
Adding 29.20 to both sides:
21 = x
Therefore, both Peter and James initially had $21 each.
To solve this problem, let's break it down step by step.
Let's start with the given information:
1) The ratio of Jim's money to Peter's money at first was 4:7.
2) After Jim spent half of his money, we need to find out how much money he had remaining.
3) Peter spent $60, and after that, he had twice as much money as Jim.
Now, let's solve the problem step by step:
Step 1: Express the ratio as a fraction.
The ratio of Jim's money to Peter's money is 4/7.
Step 2: Let's assume that Jim had x dollars at first.
So, Peter had (7/4) * x dollars because the ratio of their money is 4:7.
Step 3: Jim spent half of his money, which is (1/2) * x dollars.
Now, Jim has (1/2) * x dollars remaining.
Step 4: Peter spent $60, and now he has (7/4) * x - $60 dollars.
We are given that Peter's remaining money is twice as much as Jim's remaining money, so we can set up the equation:
(7/4) * x - $60 = 2 * ((1/2) * x)
Step 5: Solve the equation.
Applying the distributive property on the right side of the equation:
(7/4) * x - $60 = x
Multiply each term by 4 to eliminate the denominator:
7x - 240 = 4x
Subtract 4x from both sides:
3x - 240 = 0
Add 240 to both sides:
3x = 240
Divide both sides by 3:
x = 80
Step 6: Find out how much money Jim had at first.
We found that Jim had x = 80 dollars at first.
Therefore, Jim had $80 at first.