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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

Jyrki Lahtonen
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guradio
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    which is the correct solution Just check in which case one person actually got $3$ times more than the others. – dxiv Mar 13 '18 at 00:27
  • @dxiv I believe he wants to learn WHY the incorrect one is incorrect one, though. Good idea for checking the solution, though. – NL628 Mar 13 '18 at 00:27
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    @NL628 Quite possibly so, and your answer covers that part nicely (+1). However, the OP should state that into the question, and also realize that once they identified the right answer it's a lot easier to figure out where the fault lies with the wrong answer. – dxiv Mar 13 '18 at 00:30
  • True, you know better than me :D As I am new to this SE XD – NL628 Mar 13 '18 at 00:31
  • I'm not entirely sure why you think either would be correct. – fleablood Mar 13 '18 at 00:37
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    This question has nothing whatsoever to do with division algebras. Why do people select tags randomly? In particular when the tag has a wiki explaining its meaning??? – Jyrki Lahtonen Mar 13 '18 at 06:15

1 Answers1

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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.

NL628
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    I see that helps a lot I need time to tick the correct answer :) – guradio Mar 13 '18 at 00:29
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    @Guradio Thanks! I once was in middle school too :D Now I'm a high schooler, and I've done so many math competitions that I can help whenever you need! Good question :D – NL628 Mar 13 '18 at 00:30