Đáp án:
a) Gọi 3 phần được chia là a;b;c
=> a,b,c tỉ lệ thuận với 3/5; 4; 5/2 và a+b+c=213/7
$\begin{array}{l}
\Rightarrow \frac{a}{{\frac{3}{5}}} = \frac{b}{4} = \frac{c}{{\frac{5}{2}}} = \frac{{a + b + c}}{{\frac{3}{5} + 4 + \frac{5}{2}}} = \frac{3}{{7,1}} = \frac{{30}}{{71}}\\
\Rightarrow \left\{ \begin{array}{l}
a = \frac{{30}}{{71}}.\frac{3}{5} = \frac{{18}}{{71}}\\
b = \frac{{30}}{{71}}.4 = \frac{{120}}{{71}}\\
c = \frac{{30}}{{71}}.\frac{5}{2} = \frac{{75}}{{71}}
\end{array} \right.\\
b)\frac{x}{3} = \frac{{1 - y}}{4};2x = 3z \Rightarrow \frac{x}{3} = \frac{z}{2}\\
\Rightarrow \frac{x}{3} = \frac{{1 - y}}{4} = \frac{z}{2} = \frac{{3x}}{9}\\
= \frac{{z - \left( {1 - y} \right) - 3x}}{{2 - 4 - 9}}\\
= \frac{{z + y - 3x - 1}}{{ - 11}}\\
= \frac{{ - 10 - 1}}{{ - 11}} = 1\\
\Rightarrow \left\{ \begin{array}{l}
x = 3\\
1 - y = 4\\
z = 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 3\\
y = - 3\\
z = 2
\end{array} \right.
\end{array}$
Sửa :
$\begin{array}{l}
\frac{a}{{\frac{3}{5}}} = \frac{b}{4} = \frac{c}{{\frac{5}{2}}} = \frac{{a + b + c}}{{\frac{3}{5} + 4 + \frac{5}{2}}} = \frac{{\frac{{213}}{7}}}{{\frac{{71}}{{10}}}} = \frac{{30}}{7}\\
\Rightarrow \left\{ \begin{array}{l}
a = \frac{{30}}{7}.\frac{3}{5} = \frac{{18}}{7}\\
b = \frac{{30}}{7}.4 = \frac{{120}}{7}\\
c = \frac{5}{2}.\frac{{30}}{7} = \frac{{75}}{7}
\end{array} \right.
\end{array}$
