If 4a + 5b + 9c=36 and 7a + 9b + 17c=66, then a+b+c=____


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Question Number 53324 by 0955083339 last updated on 20/Jan/19

$If 4 a + 5 b + 9 c = 36 and 7 a + 9 b + 17 c = 66,$ $then a + b + c =_____.$
	Answered by Kunal12588 last updated on 21/Jan/19

	$l e t a + b + c = k$ $4 a + 4 b + 4 c + b + 5 c = 36$ $\Rightarrow 4 k + (b + 5 c) = 36 (1)$ $7 a + 7 b + 7 c + 2 b + 10 c = 66$ $\Rightarrow 7 k + 2 (b + 5 c) = 66 (2)$ $l e t b + 5 c = h$ $4 k + h = 36 [m u l t i p l y b y 2]$ $8 k + 2 h = 72$ $7 k + 2 h = 66$ $\Rightarrow k = a + b + c = 72 - 66 = 6$
	Commented by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19

	$e x c e l l e n t . . .$
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