Đáp án:
$\begin{array}{l}
a)\left( {x + y} \right).2 = 90\\
\Leftrightarrow x + y = 45\\
x:y = 7:8\\
\Leftrightarrow \dfrac{x}{7} = \dfrac{y}{8} = \dfrac{{x + y}}{{7 + 8}} = \dfrac{{45}}{{15}} = 3\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 3.7 = 21\\
y = 3.8 = 24
\end{array} \right.\\
Vậy\,x = 21;y = 24\\
b)\dfrac{x}{7} = \dfrac{y}{5} \Leftrightarrow \dfrac{x}{{21}} = \dfrac{y}{{15}}\\
\dfrac{y}{3} = \dfrac{z}{2} \Leftrightarrow \dfrac{y}{{15}} = \dfrac{z}{{10}}\\
\Leftrightarrow \dfrac{x}{{21}} = \dfrac{y}{{15}} = \dfrac{z}{{10}} = \dfrac{{x - y - z}}{{21 - 15 - 10}} = \dfrac{{ - 1}}{{ - 4}} = \dfrac{1}{4}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{1}{4}.21 = \dfrac{{21}}{4}\\
y = \dfrac{1}{4}.15 = \dfrac{{15}}{4}\\
z = \dfrac{1}{4}.10 = \dfrac{5}{2}
\end{array} \right.\\
Vậy\,x = \dfrac{{21}}{4};y = \dfrac{{15}}{4};z = \dfrac{5}{2}\\
c)\dfrac{x}{3} = \dfrac{y}{4} = \dfrac{z}{5} = \dfrac{{z - y + x}}{{5 - 4 + 3}} = \dfrac{4}{4} = 1\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 3\\
y = 4\\
z = 5
\end{array} \right.\\
Vậy\,x = 3;y = 4;z = 5
\end{array}$
