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Question Number 202566 by MASANJAJJ last updated on 29/Dec/23

	Answered by Rasheed.Sindhi last updated on 29/Dec/23

	$S e l l i n g p r i c e o f o n e t s h i r t : 7500 + p$ $w h e r e p > 0 i s p r o f i t p e r t s h i r t$ $L e t n t s h i r t s a r e s o l d; n \in N$ $T o t a l s e l l = n (7500 + p)$ $C o m m i s s i o n o f M r T o n y :$ $n (7500 + p) \times \frac{9}{100} = 297000$ $n (7500 + p) = 3300000$ $O n l y n e c e s s a r y r e s t r i c t i o n i s$ $t h a t n i s n a t u r a l a n d p i s + v e .$ $F o r e x a m p l e$ $p = 1300 \Rightarrow n = 375$ $M a n y a n s w e r s a r e p o s s i b l e .$
	Commented by Rasheed.Sindhi last updated on 29/Dec/23

	$n (7500 + p) = 3300000$ $p = \frac{3300000}{n} - 7500 < 297000 \Rightarrow n > 11$ $= \frac{440 \times 7500 - 7500 n}{n} = \frac{7500 (440 - n)}{n} \Rightarrow n < 440$ $n ∣ 7500 or n ∣ (440 - n) \Rightarrow n ∣ 440$ $n ∣ 7500 or n ∣ 440$ $W e c a n c a l c u l a t e a l l p o s s i b l e v a l u e s o f n$ $a n d t h e r e f o r e a l l c o r r e s p o n d i n g v a l u e s o f p$
	Answered by mr W last updated on 29/Dec/23

	$f o r e a c h T - s h i r t :$ $91 % c o s t \equiv t s h 7500$ $9 % c o m m i s s i o n \equiv \frac{9}{91} \times 7500 \approx 742$ $t s h 297000 c o m m i s s i o n \equiv \frac{297000}{742}$ $\approx 400 T - s h i r t s$ $\Rightarrow T o n y s o l d 400 T - s h i r t s .$
	Commented by Rasheed.Sindhi last updated on 29/Dec/23

	$Sir, I {didn}^{'} t think commission as p r o f i t .$ $but i thought it as^{'} part of {profit}^{'} . I thought$ $Mr Tony a person who sells goods on behalf$ $of an other person (original seller), b e c a u s e$ $i n m y c o u n t r y c o m m i s s i o n i s u s e d i n a b o v e$ $s e n s e . A n y w a y s i r I^{'} m n o t m u c h c o n f i d a n t!$
	Commented by mr W last updated on 29/Dec/23

	$I t h i n k t h e q u e s t i o n o n l y d e s c r i b e s$ $a s i m p l e s i t u a t i o n a s f o l l o w i n g .$ $I {d o n}^{'} t t h i n k M r T o n y h a s g o t a$ $M B A d e g r e e . H e i s j u s t a s i m p l e$ $m a n w h o s a l e s s e c o n d h a n d T - s h i r t s$ $o n t h e m a r k e t . H e p u r c h a s e s e a c h$ $T - s h i r t f o r $ 7500 f r o m a$ $w h o l e s a l e r a n d s a l e s i t f o r $ 8245 o n$ $t h e m a r k e t . H e e a r n s $ 745 f o r e a c h$ $t - s h i r t h e s o l d . H e {d o e s n}^{'} t c a r e$ $w h a t w e c a l l h i s e a r n i n g : i f a s p r o f i t$ $o r a s c o m m i s s i o n .$
	Commented by Rasheed.Sindhi last updated on 30/Dec/23

	$OK S i r, T h a n k y o u!$
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