Question

Dacă a+b+c=18 , atunci valoarea numărului N=a,(b)+b,(c)+c,(a), scris în baza zece, este :

a) 18,4 b) 20 c) 16,2 d) 22

PLUS EXPLICAȚIE VĂ ROG !!
DAU COROANĂ !!!​

Answer 1

 

$\displaystyle\bf\\Se~da\!:\\ a+b+c=18\\Se~cere\!:\\N=\overline{a,(b)}+\overline{b,(c)}+\overline{c,(a)}=?\\\\Explicatie\!:\\Numerele~de~forma\!:\\\overline{x,\!(y)}~se~vom~scrie~asa\!:\\\\\overline{x,\!(y)}=x+\overline{0,\!(y)}=x+\frac{y}{9}$

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$\displaystyle\bf\\Rezolvare:\\\\N=\overline{a,(b)}+\overline{b,(c)}+\overline{c,(a)}\\\\N=a+\overline{0,(b)}+b+\overline{0,(c)}+c+\overline{0,(a)}\\\\N=a+\frac{b}{9}+b+\frac{c}{9}+c+\frac{a}{9}\\\\N=a+b+c+\frac{a}{9}+\frac{b}{9}+\frac{c}{9}\\\\N=a+b+c+\frac{a+b+c}{9}\\\\N=18+\frac{18}{9}\\\\N=18+2\\\\\boxed{\bf N=20}\\\\Raspuns~corect~b)~20$