1
$\begingroup$

$20$ people (boys and girls) attend a dance. The first boy dances with $5$ girls; the second boy dances with $6$ girls; the third boy dances with $7$ girls, and so forth. The last boy dances with all the girls.

How many attendees are boys and how many are girls?

Any ideas or hints how to approach this question?

$\endgroup$
  • 2
    $\begingroup$ If there are $n$ boys, then the last boy dances with $n+4$ girls. If this must be the same as all the $20-n$ girls, that gives you an equation. $\endgroup$ – Henning Makholm Nov 15 '15 at 21:06
2
$\begingroup$

So the $n$th boy is dancing with $n+4$ girls. If $n$ is the last boy then there are $n+4$ girls. In total then $n + n + 4 = 20$, so $n=8$. So there are $12$ girls, $8$ boys.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.