Uneven Ratio

Algebra Level pending

At once, the ratio of male and female members on Brilliant.org was 10:1. $n$ boys joined to make the ratio 11:1, then $m$ girls joined to make the ratio 9:1. $\frac {m}{n}$ could be written as $\frac {a}{b}$ , where a and b are coprime integers. What is $ab$ ?

P.S. I made this question up, and the data in the question may not be correct.

20 22 11 9 10 18

1 solution

Margaret Zheng
Mar 16, 2016

Let the original number of male members be $90x$ and the original number of female members be $9x$ , just for the sake of getting integers when dividing.

In order for the ratio to be 11:1, there would be $9x$ more boys joining in. Now we have $99x$ : $9x$ , which is 11:1.

Then, In order for the ratio to be 9:1, there would be $2x$ more girls joining in to make the ratio $99x$ : $11x$ , which is 9:1.

Clearly, $\frac {m}{n} = \frac{2}{9}$ . Hence, $a=2$ and $b=9$ , $ab=18$ .

Uneven Ratio

1 solution

0 pending reports