[tex]\it a,\ b,\ c,\ d\in\mathbb{N}\\ \\ \\ c=\dfrac{\ 80^{(20}}{100}d=\dfrac{4}{5}d\\ \\ \\ b=\dfrac{\ 75^{(25}}{100}c=\dfrac{3}{4}c=\dfrac{3}{4}\cdot\dfrac{4}{5}d=\dfrac{3}{5}d\\ \\ \\a=\dfrac{66,(6)}{100}b=0,(6)b=\dfrac{6}{9}b=\dfrac{6}{9}\cdot\dfrac{3}{5}d=\dfrac{2}{5}d\\ \\ \\ a+b+c+d=140 \Rightarrow \dfrac{2}{5}d+\dfrac{3}{5}d+\dfrac{4}{5}d+d=140|_{\cdot5} \Rightarrow\\ \\ \\ \Rightarrow 2d+3d+4d+5d=5\cdot140 \Rightarrow 14d=5\cdot140|_{:14} \Rightarrow d=5\cdot10=50[/tex]
[tex]\it a=\dfrac{2}{5}\cdot50=20;\ \ b=\dfrac{3}{5}\cdot50=30;\ \ c=\dfrac{4}{5}\cdot50=40[/tex]
