7.
[tex]\frac{a}{3}=\frac{b}{7}=\frac{c}{8}=k\\\\\frac{a}{3}=k=>a=3k\\\\\frac{b}{7}=k=>b=7k\\\\\frac{c}{8}=k=>c=8k\\\\\\a+b+c=36\\3k+7k+8k=36\\18k=36\\k=2\\\\a=3*2=6\\b=7*2=14\\c=8*2=16[/tex]
8. Observam ca avem doua egalitati:
[tex]\frac{a}{3}= \frac{b}{5}\\\\\frac{a}{6}= \frac{c}{7}\\[/tex]
Vrem sa inmultim prima egalitate cu 1/2 ca sa putem obtine o relatie de proportionalitate intre a, b si c.
[tex]\frac{a}{3}= \frac{b}{5}[/tex] / [tex]\frac{1}{2}[/tex] => [tex]\frac{a}{6}= \frac{b}{10}[/tex]
Acum observam ca avem a/6 in ambele egalitati, iar acest lucru ne permite sa egalam cele 2 relatii intre ele:
[tex]\frac{a}{6}=\frac{b}{10}=\frac{c}{7}=k\\\\a=6k\\b=10k\\c=7k\\a+b+c=46\\6k+10k+7k=46\\23k=46\\k=2\\a=12\\b=20\\c=14[/tex]
