please help me solve this question sir. In a survey of 100 out-patients who reported at the hospital one day, It was found out that 70 coplained of fever, 50 complained of stomach ache and 30 were injured. All patients had at least one of the complaints and 44 had exactly two of the complaints. How many had all complaints?


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Question Number 52741 by Otchere Abdullai last updated on 12/Jan/19

$p l e a s e h e l p m e s o l v e t h i s q u e s t i o n s i r .$ $I n a s u r v e y o f 100 o u t - p a t i e n t s w h o$ $r e p o r t e d a t t h e h o s p i t a l o n e d a y, I t$ $w a s f o u n d o u t t h a t 70 c o p l a i n e d o f$ $f e v e r, 50 c o m p l a i n e d o f s t o m a c h$ $a c h e a n d 30 w e r e i n j u r e d . A l l$ $p a t i e n t s h a d a t l e a s t o n e o f t h e$ $c o m p l a i n t s a n d 44 h a d e x a c t l y t w o$ $o f t h e c o m p l a i n t s . H o w m a n y h a d a l l$ $c o m p l a i n t s ?$
	Answered by mr W last updated on 12/Jan/19

	$A . . . = p a t i e n t s w i t h e x a c t o n e c o m p l a i n t$ $B . . . = p a t i e n t s w i t h e x a c t t w o c o m p l a i n t s$ $C = p a t i e n t s w i t h a l l t h r e e c o m p l a i n t s$ $A_{1} + B_{1} + B_{3} + C = 70 . . . (1)$ $A_{2} + B_{1} + B_{2} + C = 50 . . . (2)$ $A_{3} + B_{2} + B_{3} + C = 30 . . . (3)$ $(1) + (2) + (3) :$ $A_{1} + A_{2} + A_{3} + 2 (B_{1} + B_{2} + B_{3}) + 3 C = 150 . . . (4)$ $A_{1} + A_{2} + A_{3} + B_{1} + B_{2} + B_{3} + C = 100 . . . (5)$ $(4) - (5) :$ $B_{1} + B_{2} + B_{3} + 2 C = 50 . . . (6)$ $B_{1} + B_{2} + B_{3} = 44 . . . (7)$ $(6) - (7) :$ $2 C = 6$ $\Rightarrow C = 3$ $i . e . t h r e e p a t i e n t s h a v e a l l c o m p l a i n t s .$
	Commented by mr W last updated on 12/Jan/19

	Commented by Otchere Abdullai last updated on 12/Jan/19

	$G o d r i c h l y b l e s s y o u s i r i n f a c t i f$ $t h e r e i s s o m e t h i n g g r e a t e r t h a n$ $b l e s s i n g t h u s w h a t i p r a y f o r y o u s i r$
	Commented by mr W last updated on 12/Jan/19

	$t h a n k y o u s i r!$
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