Question

Calculati suma tututror numerelor ab (in baza 1) , stiind ca ab(baza 10) = 3(2a + b)

Answer 1

$\overline{ab}=3(3a+b) \\ \\ 10a+b=6a+3b \\ \\ 10a-6a=3b-b \\ \\ 4a=2b \\ \\ 2a=b \\ \\ Numerele~sunt~\overline{ab} \in \{12,~24,~36,~48 \}. \\ \\ S=12+24+36+48= \\ = (12+48)+(24+36)= \\ =60+60=\boxed{120}~.$