A woman purchased a number of plates for$150.00. Four of the plates got broken while transporting themto her shop. By selling the remaining plates at a profit of $ 1.00 on each, she made a total profit of $6.00. How many plates did she purchase?


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Question Number 108917 by pete last updated on 20/Aug/20

$A woman purchased a number of plates$ $for $ 150 . 00 . Four of the plates got broken$ $while transporting themto her shop . By selling$ $the remaining plates at a profit of $ 1.00 on each,$ $she made a total profit of $ 6.00 . How many$ $plates did she purchase ?$
	Answered by nimnim last updated on 20/Aug/20

	$L e t t h e t o t a l n u m b e r o f p l a t e s b e x$ $t h e n C P o f 1 p l a t e = $ \frac{150}{x}$ $s i n c e 4 p l a t e s h a d b e e n b r o k e n,$ $S P o f (x - 4) p l a t e s \Rightarrow (x - 4) (\frac{150}{x} + 1) = 156$ $\Rightarrow x^{2} + 146 x - 600 = 156 x$ $\Rightarrow x^{2} - 10 x - 600 = 0$ $\Rightarrow (x - 30) (x + 20) = 0$ $\Rightarrow x = 30 o r x = - 20 (n e c l e g t e d)$ $H e n c e, t h e w o m a n p u r c h a s e d 30 p l a t e s$
	Commented by pete last updated on 20/Aug/20

	$iThank you sir$
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