Question

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

Answer 1

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