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Question Number 20364 by mondodotto@gmail.com last updated on 26/Aug/17

Answered by Tinkutara last updated on 26/Aug/17

59 = 77 − (6 + 3x) + x 2x = 12 x = 6

$$\mathrm{59}\:=\:\mathrm{77}\:−\:\left(\mathrm{6}\:+\:\mathrm{3}{x}\right)\:+\:{x} \\ $$$$\mathrm{2}{x}\:=\:\mathrm{12} \\ $$$${x}\:=\:\mathrm{6} \\ $$

Commented by $@ty@m last updated on 26/Aug/17

Can you pl. explain 3x and x.

$${Can}\:{you}\:{pl}.\:{explain}\:\mathrm{3}{x}\:{and}\:{x}. \\ $$

Commented by Tinkutara last updated on 26/Aug/17

Commented by Tinkutara last updated on 26/Aug/17

n(P∪H∪W) = n(P) + n(H) + n(W) − n(P∩H) − n(H∩W) − n(P∩W) + n(P∩H∩W) Given that n(P∪H∪W) = 59 and a + b + c = 6 so that n(P∩H) + n(H∩W) + n(P∩W) = (a + x) + (c + x) + (b + x) = a+b+c+3x = 3x + 6 and n(P∩H∩W) = x.

$${n}\left(\mathrm{P}\cup\mathrm{H}\cup\mathrm{W}\right)\:=\:{n}\left(\mathrm{P}\right)\:+\:{n}\left(\mathrm{H}\right)\:+\:{n}\left(\mathrm{W}\right) \\ $$$$−\:{n}\left(\mathrm{P}\cap\mathrm{H}\right)\:−\:{n}\left(\mathrm{H}\cap\mathrm{W}\right)\:−\:{n}\left(\mathrm{P}\cap\mathrm{W}\right)\:+ \\ $$$${n}\left(\mathrm{P}\cap\mathrm{H}\cap\mathrm{W}\right) \\ $$$$\mathrm{Given}\:\mathrm{that}\:{n}\left(\mathrm{P}\cup\mathrm{H}\cup\mathrm{W}\right)\:=\:\mathrm{59}\:\mathrm{and} \\ $$$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{6}\:\mathrm{so}\:\mathrm{that} \\ $$$${n}\left(\mathrm{P}\cap\mathrm{H}\right)\:+\:{n}\left(\mathrm{H}\cap\mathrm{W}\right)\:+\:{n}\left(\mathrm{P}\cap\mathrm{W}\right)\:= \\ $$$$\left({a}\:+\:{x}\right)\:+\:\left({c}\:+\:{x}\right)\:+\:\left({b}\:+\:{x}\right)\:=\:{a}+{b}+{c}+\mathrm{3}{x} \\ $$$$=\:\mathrm{3}{x}\:+\:\mathrm{6} \\ $$$$\mathrm{and}\:{n}\left(\mathrm{P}\cap\mathrm{H}\cap\mathrm{W}\right)\:=\:{x}. \\ $$

Commented by $@ty@m last updated on 26/Aug/17

Thank you.

$${Thank}\:{you}. \\ $$

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