At a party with “m” people, a lady dances with p gentlemen, the second with p + 1, the third one with p + 2, and so on until the last one dances with all the gentlemen, find the number of ladies who attended the party in terms of “m”and “p”.


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Question Number 185515 by HeferH last updated on 23/Jan/23

$A t a p a r t y w i t h ‘ ‘ m^{″} p e o p l e, a l a d y d a n c e s$ $w i t h p g e n t l e m e n, t h e s e c o n d w i t h p + 1,$ $t h e t h i r d o n e w i t h p + 2, a n d s o o n u n t i l t h e$ $l a s t o n e d a n c e s w i t h a l l t h e g e n t l e m e n,$ $f i n d t h e n u m b e r o f l a d i e s w h o a t t e n d e d t h e$ $p a r t y i n t e r m s o f ‘ ‘ m^{″} a n d ‘ ‘ p^{″} .$
	Answered by manxsol last updated on 23/Jan/23

	$l + g = m$ ${l a d i e}_{l} \Rightarrow {g e n t l e m a n}_{p + l - 1}$ $p + l - 1 = g$ $l + p + l - 1 = m$ $2 l + p - 1 = m$ $l = \frac{m + 1 - p}{2}$
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