Question

Aflati numerele x si y, stiind ca sunt invers proportionale cu 4 si 6 si ca c.m.m.d.c al lor este 30.

Answer 1

x·4=y·6=k
⇒x·4=k⇒x=k/4;
⇒y·6=k⇒y=k/6;
⇒c.m.m.m.d.c=30 ,unde c.m.m.d.c este cel mai mare divizor comun];
⇒[x;y]=[k/4;k/6]⇒[3k/12;2k/12]⇒[3k/12-2k/12]⇒k/12=30
⇒k/12=30⇒k=12·30⇒k=360;
⇒x=k/4⇒x=360/4⇒x=90;
⇒y=k/6⇒y=360/6⇒y=60;