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If example says, there are total 1600 people. from total, man is 15% more than women... how to find number of man and women from 1600?

What I did is:

  1. 100 - 15 = 85
  2. Divide 85/2 = 42.5
  3. 42.5% of 1600 = 680
  4. 680 + 680 = 1360. 1600 - 1360 = 240
  5. Man = 680 + 240 = 920
  6. Women = 680

I know there can be better way, can someone help me?

Amit3581
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1 Answers1

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You'd get it easier using a system of equations.

Making the most of the chromosome distinction, let $x$ be the numebr of women and $y$ the numebr of men.

The total people is 1600: $x+y=1600$

And men are 15% more than women, that is, $y=1,15 \cdot x$ (because 15% more = 100% + 15% = 115% = 115/100).

Consequently, if you replace above, you'll have

$x+1,15 x = 1600 \Rightarrow 2,15x=1600 \ \Rightarrow \ x= \frac{1600}{2,15}=744,18$

This is obviously impossible, which makes me think I've misunderstood your question. Re-reading it, I could have also understood that "15% of the total is the difference between men and women", (being more men), but it should have been clearer.

In that case, you write

$0,15\cdot 1600 = y-x$

and that's your second equation. By the way, 15% of 1600 is 240.

So your both equations are $x+y=1600$ and $y-x=240$.

This is a very easy system whose solution is $y=920$ men and $x=680$ women.

FGSUZ
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