Tìm x,y,z biết a)x/y=7/13 và x+y=16 b)x/y=9/10 và y-x=120 c)x/30=y/10=z/6 và x+y+z=92 d)x/2=y/3=z/4 và x+y+z=81 e)x/4=y/12=z/15 và y-x=4 f)x/3=y/4 và

Đáp án:

$\begin{array}{l}
a)\dfrac{x}{y} = \dfrac{7}{{13}}\\
 \Rightarrow \dfrac{x}{7} = \dfrac{y}{{13}} = \dfrac{{x + y}}{{7 + 13}} = \dfrac{{16}}{{20}} = \dfrac{4}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{28}}{5}\\
y = \dfrac{{52}}{5}
\end{array} \right.\\
Vay\,x = \dfrac{{28}}{5};y = \dfrac{{52}}{5}\\
b)\dfrac{x}{y} = \dfrac{9}{{10}}\\
 \Rightarrow \dfrac{x}{9} = \dfrac{y}{{10}} = \dfrac{{y – x}}{{10 – 9}} = \dfrac{{120}}{1} = 120\\
 \Rightarrow \left\{ \begin{array}{l}
x = 1080\\
y = 1200
\end{array} \right.\\
c)\dfrac{x}{{30}} = \dfrac{y}{{10}} = \dfrac{z}{6} = \dfrac{{x + y + z}}{{30 + 10 + 6}} = \dfrac{{92}}{{46}} = 2\\
 \Rightarrow \left\{ \begin{array}{l}
x = 60\\
y = 20\\
z = 12
\end{array} \right.\\
d)\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} = \dfrac{{x + y + z}}{{2 + 3 + 4}} = \dfrac{{81}}{9} = 9\\
 \Rightarrow \left\{ \begin{array}{l}
x = 18\\
y = 27\\
z = 36
\end{array} \right.\\
e)\dfrac{x}{4} = \dfrac{y}{{12}} = \dfrac{z}{{15}} = \dfrac{{y – x}}{{12 – 4}} = \dfrac{4}{8} = \dfrac{1}{2}\\
 \Rightarrow \left\{ \begin{array}{l}
x = 2\\
y = 6\\
z = \dfrac{{15}}{2}
\end{array} \right.\\
f)\dfrac{x}{3} = \dfrac{y}{4} = \dfrac{{2x}}{6} = \dfrac{{5y}}{{20}} = \dfrac{{2x + 5y}}{{6 + 20}} = \dfrac{{10}}{{26}} = \dfrac{5}{{13}}\\
 \Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{15}}{{13}}\\
y = \dfrac{{20}}{{13}}
\end{array} \right.\\
g)\dfrac{x}{y} = \dfrac{3}{4}\\
 \Rightarrow x = \dfrac{3}{4}y\\
Do: – 3 + 5y = 33\\
 \Rightarrow 5y = 36\\
 \Rightarrow y = \dfrac{{36}}{5}\\
 \Rightarrow x = \dfrac{3}{4}y = \dfrac{3}{4}.\dfrac{{36}}{5} = \dfrac{{27}}{5}\\
h)8x = 5y\\
 \Rightarrow \dfrac{x}{5} = \dfrac{y}{8} = \dfrac{{2x}}{{10}} = \dfrac{{y – 2x}}{{8 – 10}} = \dfrac{{ – 10}}{{ – 2}} = 5\\
 \Rightarrow \left\{ \begin{array}{l}
x = 25\\
y = 40
\end{array} \right.
\end{array}$