Question

sa se imparta nr 36 in 2 parti invers proportionale cu 4 si 5

Answer 1

[tex]\{a,b\} i.p.\{4,5\}\Rightarrow \frac{a}{\frac{1}{4}}=\frac{b}{\frac{1}{5}}=k\Rightarrow a=\frac{k}{4},b=\frac{k}{5}\\ a+b=36\\ \frac{k}{4}+\frac{k}{5}=36|\cdot 20\\ 5k+4k=720\\ 9k=720\\ \boxed{k=80}\\ a=\frac{k}{4}\Rightarrow \boxed{a=20}\\ a=\frac{k}{5}\Rightarrow \boxed{b=16}[/tex]