Question

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?
j/p = 4/7
(j - j/2)/(p-60) = 1/2

(j/2)/(7j/4 - 60) = 1/2
4j = 7j-240
j = 80


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.

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