a+b=84(2)
{a;b}i.p{5;3}==>a/1/5=b/1/3=k[tex] \left \{ {{a= \frac{k}{5} } \atop {b= \frac{k}{3} }} \right. [/tex](1)
(1) in (2)
[tex] \frac{k}{5}+ \frac{k}{3} =84 [/tex]
divizorul comun este 15 asa ca amplificam prima fractie cu trei si a doua cu 5
[tex] \frac{3k}{15}+ \frac{5k}{15}=84[/tex][tex] \frac{8k}{15}=84 [/tex]
8k=84x15
8k=1260
k=157.5
a=157.5:5=31.5
b=157.5:3=52.5
