In a box, the number of blue counters and the number of green counters are in the ratio 7:4. The number of green counters and the number of red counters are in the ratio 3:1. The total number of counters in the box is 444. How many green counters are in the box?

Calculate the total number of parts in the ratio. Determine the total number of green and red counters, which are 4 parts out of a total of 11. Multiply this fraction by the total number of counters (444) to get the total number of green and red counters. The number of green counters is 3 parts out of this total, so a similar multiplication gives the number of green counters.

Explanation:

The problem involves the concept of ratios and arithmetic. We need to solve the question in two stages:

Firstly, the question tells us that the number of blue counters and green counters are in the ratio 7:4. This implies, for every 7 blue counters, there are 4 green ones. Therefore, the total number of blue and green counters together can be thought of as 7+4 which equals 11 parts.
Secondly, the number of green counters and red counters are in the ratio 3:1. Therefore, the total number of green and red counters together equals 3+1, which is equal to 4 parts. We're given that the total number of green, red, and blue counters is 444. Now, going back to the first step the blue counters are 7 parts out of 11. The green and red counters combined are 4 parts out of 11. So, the total of green and red counters is 4/11 * 444 = 161.04. But since we can't have 0.04 of a counter, it rounds to 161. Now, given that the green counters and red counters are in the ratio 3:1, so out of the total 161, the green counters are 3/4 * 161 = 120.75, which rounds to 121. So there are 121 green counters in the bag.

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