# 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?

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1. 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 :)

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2. 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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