[tex]8a=4,5b =k \Rightarrow a= \frac{k}{8}~si~b= \frac{k}{4,5}= \frac{k}{ \frac{9}{2} }= \frac{2k}{9}. \\ \\ m_a(a,b)= \frac{a+b}{2}=200 \Leftrightarrow \frac{ \frac{k}{8}+ \frac{2k}{9} }{2}=200 \Rightarrow \frac{k}{8 }+ \frac{2k}{9} =400. \\ \\ Inmultim~cu~72,~si~obtinem:~9k+16k=400 \cdot 72 \Leftrightarrow \\ \\ \Leftrightarrow 25k=25 \cdot 1152 \Rightarrow k=1152. \\ \\ Deci~a= \frac{1152}{8} = 144~si~b= \frac{2 \cdot 1152}{9}= 256. \\ \\ Observatie:~b~putea~fi~calculat~mai~rapid~din~b=400-a.[/tex]
