Question

Aflati numerele a si b, stiind ca sunt invers proporționale cu 0,2 si 0,5 , iar 4a+3b=78.

Answer 1

[tex]\{a,b\}i.p.\{0,2;0,5\}\Rightarrow\frac{a}{\frac{1}{\frac{1}{5}}}=\frac{b}{\frac{1}{\frac{1}{2}}}\Rightarrow \frac{a}{5}=\frac{b}{2}=k\Rightarrow a=5k,b=2k\\ 4a+3b=78\\ 20k+6k=78\\ 26k=78\\ \boxed{k=3}\\ a=5k\Rightarrow \boxed{a=15}\\ b=2k\Rightarrow \boxed{b=6}\\ [/tex]