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The ratio of the number of balls Miko had to the number of balls Cheko had was 7 : 4 at first.Miko gave 24 balls to his friends and the ratio of Miko’s balls to Cheko’s balls became 9 : 12.How many balls did Miko have at first?

Question

The ratio of the number of balls Miko had to the number of balls Cheko had was 7 : 4 at first.Miko gave 24 balls to his friends and the ratio of Miko’s balls to Cheko’s balls became 9 : 12.How many balls did Miko have at first?

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Solution

Let's solve this step by step:

Step 1: Let's assume the initial number of balls Miko had was 7x and the number of balls Cheko had was 4x.

Step 2: According to the problem, Miko gave away 24 balls, so he now has 7x - 24 balls.

Step 3: After giving away the balls, the ratio of Miko's balls to Cheko's balls became 9 : 12. So, we can write this as (7x - 24) / 4x = 9 / 12.

Step 4: Simplify the equation. Cross multiply to get rid of the fraction: 12 * (7x - 24) = 9 * 4x.

Step 5: This simplifies to 84x - 288 = 36x.

Step 6: Solve for x by subtracting 36x from both sides: 84x - 36x = 288, which simplifies to 48x = 288.

Step 7: Solve for x by dividing both sides by 48: x = 288 / 48 = 6.

Step 8: Substitute x = 6 back into the equation for the number of balls Miko had at first (7x), we get 7 * 6 = 42.

So, Miko had 42 balls at first.

This problem has been solved

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