x·2=y·5=z·6=k
⇒x·2=k⇒x=k/2;
⇒y·5=k⇒y=k/5;
⇒z·6=k⇒z=k/6;
⇒x+y+z=420
⇒k/2+k/5+k/6=420
⇒15k/30+6k/30+5k/30=420
⇒26k/30=420⇒26k=420·30
⇒26k=12600
⇒k=12600/26
⇒k=6300/13;
⇒x=k/2⇒x=6300/13/2⇒x=6300/2·13⇒x=6300/26⇒x=3150/13;
⇒y=k/5⇒y=6300/13/5⇒y=6300/5·13⇒y=6300/65⇒y=1260/13;
⇒z=k/6⇒z=6300/13/6⇒z=6300/6·13⇒z=6300/78⇒z=1050/13;
