College Algebra, Chapter 1, 1.2, Section 1.2, Problem 62

Suppose that a plank $30 ft$ long rests on top of a flat roofed building, with $5 ft$ of the plank projecting over the edge. A worker weighing $240 lb$ sits on one end of the plank. What is the largest weight that can be hung on the projecting end of the plank if it is to remain in balance?

By using the law of lever, let $w_1$ be the weight of the man, $x_1$ be the distance to the edge of the building, $w_2$ be the required weight to balance and $x_2$ be the other end of the plank. So in order to remain in balance..


$
\begin{equation}
\begin{aligned}

w_1 x_1 =& w_2 x_2
\\
\\
240 lb (30 - 5) =& w_2(5)
\\
\\
240(25) =& w_2(5) \qquad \text{Solve for } w_2
\\
\\
w_2 =& 1200 lbs

\end{aligned}
\end{equation}
$