Final answer:
To solve the problem, we used algebraic methods to find the common multiplier for the initial ratio of balls Miko and Cheko had. Miko had 56 balls before he gave any away.
Step-by-step explanation:
The question asks to determine how many balls Miko had originally based on given ratios before and after he gave away some balls. To solve this problem, we set up two ratio equations to represent the relationship between the number of balls Miko and Cheko had.
Initially, the ratio of Miko's balls to Cheko's balls is 7:4. Let's represent the number of balls Miko had as 7x and the number of balls Cheko had as 4x. The variable 'x' is a common multiplier for the ratio.
After Miko gave away 24 balls, the new ratio became 9:12, equivalent to 3:4 after simplifying. Now, Miko has (7x - 24) balls and Cheko still has 4x balls. Setting up the ratio equation, we get (7x - 24)/4x = 3/4.
Cross-multiplying gives us 4(7x - 24) = 3(4x), which simplifies to 28x - 96 = 12x. Solving for 'x' gives us x = 8.
Originally, Miko had 7x balls, so we substitute 'x' with 8 to get the total number of balls Miko had at first: 7 * 8 = 56 balls.
Therefore, Miko initially had 56 balls.