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I will create two simple examples to explain the problem.

In this problem you have the following variables:

  • Amount: 150£

  • Buckets: 4

  • Percentage increase: 50%

Each bucket have one number [1, 2, 3, 4].

You want to put 50% more money in the odd buckets but you want to keep the total amount the same as before (150).

The second problem is the same but with different variables:

  • Amount: 150£
  • Buckets: 3
  • Percentage increase: 50%

Each bucket have one number [1, 2, 3].

What is the calculation to solve those two problems? Can the calculation works with different variables values?

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I tried to write down the first example without using variables and hope it explaines the process.

The first thing to work out is finding the factor between the amount of the first bucket and the total amount. Lets say the first bucket has $100\%$, with a 50% increase the second bucket will have $(100\% + 50\%)\cdot 100\% = 150%$ of the first bucket. The third bucket will have $(100\% + 50\%)\cdot 150\% = 225\%$. And similarly the third bucket will contain $(100\% + 50\%)\cdot 225\% = 337.5\%$.

In total we need $100\% + 150\% + 225\% + 337.5\% = 812.5\% = 8.125$ which corresponds to 150£.

To find out how much we have in the first bucket, we have to find how much corresponds to $100\%$, which we can do by dividing by $812.5\% = 8.125$, which is $18.46...£$.

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What about this solution?

Data:

Amount = 150£

Odd count = 2

Even count = 2

percentage increase on odd= 100%

Proportion:

odd = 2x

even = x

Calculation:

2 * (x) + 2 * (2x)= 150£

2x + 4x = 150£

6x = 150£

x = 25


odd = 50

even = 25

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