The ratio of Jim's money to Peters money was 4:7 at first. After peter gave 3/14 of his money to jim, they have equal amounts of money. 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.
To find out how much money Jim had at first, we need to follow these steps:
Step 1: Let's assume Jim initially had x amount of money.
Step 2: Peter initially had 7/4 times the amount of money Jim had, so Peter had (7/4)x amount of money.
Step 3: Peter gave 3/14 of his money to Jim, which means Jim received (3/14)(7/4)x = (21/56)x amount of money.
Step 4: After this exchange, both Jim and Peter now have an equal amount of money, so we can set up the equation:
x + (21/56)x = (7/4)x
Step 5: Simplify the equation:
(56/56)x + (21/56)x = (7/4)x
(77/56)x = (7/4)x
Step 6: Divide both sides of the equation by (7/4) to solve for x:
(77/56)x / (7/4) = x
(77/56) * (4/7) = x
(11/2) = x
Step 7: Simplify:
x = 11/2
x = 5.5
Therefore, Jim had 5.5 units of money at first.
To solve this problem, let's first set up a system of equations based on the given information:
Let's assume that the initial amount of money Jim had is represented by '4x', and the initial amount of money Peter had is represented by '7x'.
According to the problem, Peter gives 3/14 of his money to Jim, which means Jim receives (3/14) * 7x from Peter.
After this exchange, both Jim and Peter have equal amounts of money. We can set up the equation:
Jim's money after the exchange = Peter's money after the exchange
4x + (3/14) * 7x = 7x - (3/14) * 7x
Multiplying by 14 to clear the fraction, we get:
56x + 3 * 7x = 98x - 3 * 7x
Simplifying the equation:
56x + 21x = 98x - 21x
77x = 77x
We can see that the equation is true for any value of x. However, we need to find the initial amount of money Jim had, so we can assume x = 1 to simplify the calculation.
Therefore, Jim had 4x = 4 * 1 = 4 units of money at first.
Thus, Jim had 4 units of money initially.
J/P = 4/7 so J = 4 P/7
P - 3 P/14 = J + 3 P/14
P - 3 P/7 = J = 4 P/7
4 P/7 = 4 P/7
any P OR any J
say J = 8
then P = 14
14 -3 (14/14) = ?? 8 + 3(14/14)
well
11 = 11 sure enough :)