I feel like this should be obvious, but I am still struggling to wrap my head around this:
Suppose Bill has $1000$ apples and $2000$ oranges, while Sue has $1500$ apples and 500 oranges. Now suppose we want to take $200$ apples and $500$ oranges total away from both of them in such a way as to keep the amount proportional to the amount that they both have to start.
If we calculate the percent of the total of each that we need to take away we can take the same percent from each person: \begin{align} \frac{200 \,\,\text{apples}}{2500\,\,\text{apples}} &= 8 \% \\ 8\%\,\,\text{of}\,\,1000\,\,\text{apples} &= 80\,\,\text{apples} \\ 8\%\,\,\text{of}\,\,1500\,\,\text{apples} &= 120\,\,\text{apples} \\ \\ \frac{500\,\,\text{oranges}}{2500 \,\,\text{oranges}} &= 20\% \\ 20\%\,\,\text{of}\,\,2000\,\,\text{oranges} &= 400\,\,\text{oranges} \\ 20\%\,\,\text{of}\,\,500\,\,\text{oranges} &= 100\,\,\text{oranges} \end{align} In summary, the result looks like this:
| Bill | Sue | |
|---|---|---|
| Apples | 80 | 120 |
| Oranges | 400 | 100 |
| Total | 480 | 220 |
Now suppose say we instead just want $700$ fruit: \begin{align} \frac{700\,\,\text{fruit}}{5000\,\,\text{fruit}}&= 14\% \\ 14\%\,\,\text{of}\,\,3000&=420 \\ 14\%\,\,\text{of}\,\,2000&=280 \end{align}
| Bill | Sue | |
|---|---|---|
| Fruit | 420 | 280 |
We are now taking a different amount of total fruit from each person. This is counter-intuitive to me for some reason.
Can anyone explain why this happens? Which method is the most fair, or does it depend on the value of each fruit? Or is there a better way to calculate this?