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Ken and Gary had some money. The ratio of the amount of money Ken had to the amount of money Gary had was 5 : 4. Ken then gave $63 to Gary. The ratio of the amount of money Ken had to the amount of money Gary had became 2 : 3.How much did Gary have in the end?

Question

Ken and Gary had some money. The ratio of the amount of money Ken had to the amount of money Gary had was 5 : 4. Ken then gave $63 to Gary. The ratio of the amount of money Ken had to the amount of money Gary had became 2 : 3.How much did Gary have in the end?

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Solution

Let's solve this step by step:

Step 1: Let's assume the initial amount of money Ken had was 5x and the amount Gary had was 4x.

Step 2: According to the problem, Ken gave $63 to Gary. So, Ken now has 5x - 63 and Gary has 4x + 63.

Step 3: After giving $63 to Gary, the ratio of Ken's money to Gary's money became 2 : 3. So, we can write the equation as (5x - 63) / (4x + 63) = 2 / 3.

Step 4: Cross multiply to solve for x. We get 15x - 189 = 8x + 126.

Step 5: Simplify the equation to find the value of x. We get 7x = 315, so x = 45.

Step 6: Substitute x = 45 back into 4x + 63 to find the final amount of money Gary has. We get 4*45 + 63 = $243.

So, Gary had $243 in the end.

This problem has been solved

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