I have 2139 and I want to divide it into 10 people where 1 should get 3 times more than the 9 other. Solutions below:
Solution A:
What I did is get 30% of the total and give it to the that person and divide the rest to 9 equally solution is
2139 * 30% = 641.70
2139 - 641.70 = 1494.3
1494.3 / 9 = 166.03
Person who gets 3 times more will get 641.70
Other 9 will get 166.03
Solution B:
What I did is divide the total by 12 then multiply the result by 3 that will be the amount to the person who will get 3 times more.
2139 / 12 = 178.25
178.25 * 3 = 534.75
Person who gets 3 times more will get 534.75
Other 9 will get 178.25
I am wondering which is the correct solution. I am confused why get the different outcome for Solution A and Solution B
Solution A is incorrect because the one with the most does NOT get $30\%$ of the total. In fact, assume that that person gets $3x$ things and the other $9$ people each get $x$ things. Then, the total is $3x + 9x = 12x$. Thus, $\frac{3x}{12x}$ is the percentage that the first guy gets, which is actually $25\%$ not $30\%$
Thus, the Solution A is incorrect and the Solution B is correct.