Question

̧tiind ca ̆ numerele naturale a, b, c verifica ̆ rela ̧tiile 3 × a + b = 11 ̧si 12 × a + 4 × b + c = 50, calcula ̧ti 3 × a × c + b × c.

Answer 1

$\displaystyle\\\begin{cases} 3a+b=11|\cdot 4 \\ 12a+4b+c=50\end{cases} \Leftrightarrow \begin{cases} 12a+4b=44~(1) \\ 12a+4b+c=50~(2) \end{cases}.\\\textnormal{Scadem~relatiile~(1)~si~(2)} ~: (12a+4b)+c-(12a+4b)\\=c=50-44=6,~\textnormal{deci},~\boxed{c=6}.\\\textnormal{Asadar,~3ac+bc=c(3a+b)=}~6\cdot11=\boxed{66}~.$