A company produces red, green and blue buckets in the ratio $2:7:4$. If a week's production totals $7,774$ buckets, how many green buckets are produced?

Let the production of Red, green and Blue bucket is 2x, 7x and 4x respectively.
Week's total buckets production $=7,774$

$\begin{array}{l}\therefore 2x+7x+4x\\ =7,774\\ 13x=7,774\\ \Rightarrow x=\frac{7774}{13}\end{array}$

$\Rightarrow x=598$

$\therefore$ Production of green bucket $=7x$

$$\begin{gathered} =7\times 598 \\ =4186 \end{gathered}$$