Question

Determinati cifra ''a'' din egalitatea 577a+aaa=6666(in baza zece)

Answer 1

577a+aaa=6666
⇒5·1000+7·100+7·10+a+100a+10a+a=6·1000+6·100+6·10+6
⇒5000+700+70+112a=6000+600+60+6
⇒singura varianta care rezolva solutia este a=8;
⇒5000+700+70+112·8=6666
⇒5000+700+70+896=6666
⇒6666=6666⇒adevarat unde a-cifra⇒a∈N⇔a=8;

Answer 2

$~~~~\overline{577a}+ \overline{aaa}=6666 \Leftrightarrow \\ \Leftrightarrow 5770+a+111a=6666 \Leftrightarrow \\ \Leftrightarrow 5770+112a=6666 \Leftrightarrow \\ \Leftrightarrow 112a=6666-5770 \Leftrightarrow \\ \Leftrightarrow 112a=896 \Rightarrow \boxed{a=8}. \\ \\ \underline{Solutie}:~\boxed{ \bold{ a=8 }}.$