The ratio of Jim's 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.