The cost of maintaining a school is partly constant and partly varies as the number of students. With 50 students the cost is $15705 and with 40 students the cost is $13305. If the fee per student is $360.00, what is the least number of students for which the school can be run without loss?


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Question Number 209065 by necx122 last updated on 01/Jul/24

$T h e c o s t o f m a i n t a i n i n g a s c h o o l i s$ $p a r t l y c o n s t a n t a n d p a r t l y v a r i e s a s$ $t h e n u m b e r o f s t u d e n t s . W i t h 50 s t u d e n t s$ $t h e c o s t i s $ 15705 a n d w i t h 40 s t u d e n t s$ $t h e c o s t i s $ 13305 . I f t h e f e e p e r s t u d e n t$ $i s $ 360.00, w h a t i s t h e l e a s t n u m b e r o f$ $s t u d e n t s f o r w h i c h t h e s c h o o l c a n b e$ $r u n w i t h o u t l o s s ?$
	Answered by mr W last updated on 01/Jul/24

	$C o s t = a + b x w i t h x = n u m b e r o f s t u d e n t s$ $15705 = a + 50 b$ $13305 = a + 40 b$ $\Rightarrow b = 240, a = 3705$ $F e e = 360 x$ $F e e ⩾ C o s t$ $360 x ⩾ 3705 + 240 x$ $\Rightarrow x ⩾ 30.9 \Rightarrow a t l e a s t 31 s t u d e n t s$
	Commented by necx122 last updated on 01/Jul/24

	$T h a n k y o u s i r .$
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