Let $a$ be the amount of mixture taken from glass 1 and $b$ be the same taken from glass 2.
$$\begin{equation} \frac{1} {1+2} \times a + \frac{4 }{4+1} \times b = \frac{2} {1+2} \times a + \frac{1} {4+1} \times b \\\implies \frac{a} {3} = \frac{3b} {5} \label{628eq1} \end{equation}$$
$$\begin{equation} a+b = 280 \label{628eq2} \end{equation}$$
From $\ref{628eq1}$ and $\ref{628eq2}$,
$$\frac{a}{3} = \frac{3(280-a)}{5} \\ \implies 5a = 9\times280 - 9a \\\implies a = 180.$$