Question

Determinati numerele rationale pozitive a, b, c, stiind ca sunt direct proportionale cu numerele 5, 6, si 10, si ca 5a + 2b - 3c= 84

Answer 1

a/5=b/6=c/10=k
⇒a/5=k⇒a=5k;
⇒b/6=k⇒b=6k;
⇒c/10=k⇒c=10k;
⇒5a+2b-3c=84
⇒5·5k+2·6k-3·10k=84
⇒25k+12k-30k=84
⇒37k-30k=84
⇒7k=84
⇒k=12;
⇒a=12·5=60;
⇒b=12·6=72;
⇒c=12·10=120;

Answer 2

a=5k b=6k c=10k 5a+2b-3c=84 <=> 5×5k+2×6k-3×10k=84 <=> 25k+12k-30k=84 <=> 7k=84 <=> k=12 => a=5×12=60 b=6×12=72 c=10×12=120.