Question

Numerele naturale a,b sunt direct proportionale cu 11,respectiv4. Aflati a si b stiind ca impartind nr a la b obtinem catur 2 si restul 30 adica (a:b=2r30)

Answer 1

$a;b \ \ \ d.p. \\ 11;4 \\\\\\ \Longrightarrow \frac{a}{11}=\frac{b}{4}=k \\\\\\ a=11k\\b=4k \\\\\\ a:b=2 \ rest \ 30 \\\\ a=2b+30 \\\\\\ 11k=2*4k+30 \\\\ 11k=8k+30 \\\\ 11k-8k=30 \\\\ 3k=30 \ \ \ |:3 \\\\ \underline{k=10} \\\\\\ a=11*10 \\\\ \boxed{a=110} \\\\\\ b=4*10 \\\\ \boxed{b=40}$