Question

Numerele a,b,c sunt invers proportionale cu 3/4,5/3,7/36 si 3a+5b+7c=66.Aflati a, b si c.

Answer 1

{a,b,c}ip{3/4,5/3,7/36}
3a/4=5b/3=7c/36=k
3a/4=k⇒a=4k/3
5b/3=k⇒b=3k/5
7c/36=k⇒c=36k/7
inlocuim in relatia 3a+5b+7c=66
3·4k/3+5·3k/5+7·36k/7=66    simplificam
4k+3k+36k=66
43k=66
k=66/43
a=4k/3=(4·66/43)/3=264/(43·3)=264/129
b=3k/5=(3·66/43)/5=198/215
c=36k/7=(36·66/43)/7=2376/301