Avem fractiile de forma a/x ; b/y ; c/z si stim :
a/2=b/3=c/5=k =>a=2k ; b=3k ; c=5k
Si mai stim, de asemenea ca :
x/3=y/5=z/6=k' =>x=3k' ; y=5k' ; z=6k'
Problema ne mai spune ca a/x + b/y + c/z = 3/10, adica :
2k/3k' + 3k/5k' + 5k/6k' = 3/10
Aducem la numitor comun, 30k'
20k+18k+25k=9k'
63k=9k' =>k'=7k
Rescriem proportiile numitorilor : x/3=y/5=z/6=7k
Avem x=21k ; y=35k ; z=42k
=>a/x devine 2k/21k=2/21
=>b/y devine 3k/35k=3/35
=>c/z devine 5k/42k=5/42
Facand proba, avem 2/21 + 3/35 + 5/42 =
Numitor comun 210
(20+18+25)/210 = 63/210 = 3/10 Adevarat
