In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
Question
In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
Solution
Let's denote the number of balls in each box as follows: R for the red box, G for the green box, and B for the blue box.
From the problem, we know two things:
- B = 2R (there are twice as many balls in the blue box as there are in the red box)
- G + R = 2B (there are twice as many balls in the green and red boxes combined as there are in the blue box)
We can substitute B from the first equation into the second equation to get G + R = 2(2R) = 4R. Simplifying this gives G = 4R - R = 3R.
We also know that the total number of balls is 108, so R + G + B = 108. Substituting B and G from the previous equations gives R + 3R + 2R = 108, which simplifies to 6R = 108. Solving for R gives R = 18.
Substituting R = 18 into the equation G = 3R gives G = 3*18 = 54.
So, there are 54 balls in the green box.
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