Question

Trei numere naturale au media aritmetica egala cu 310 si sunt invers proportionale cu 2;3;5.Aflati numerele.

Answer 1

[a+b+c]/3=310
⇒a+b+c=3·310
⇒a+b+c=930;
⇒a·2=b·3=c·5=k
⇒a·2=k⇒a=k/2;
⇒b·3=k⇒b=k/3;
⇒c·5=k⇒c=k/5;
⇒k/2+k/3+k/5=930
⇒15k/30+10k/30+6k/30=930
⇒31k/30=930
⇒k=30·930/31
⇒k=30·30
⇒k=900;
⇒a=900/2⇒a=450;
⇒b=900/3⇒b=300;
⇒c=900/5⇒c=180;