Answer
The ball is dropped from $80\text{ inches}$ such that it bounces 56 inches.
Work Step by Step
Consider that the height by which the ball bounces is B and the height from which the ball is dropped is D. It is provided that the variable B varies directly as D, that is $B\ =\ kD$.
Thus,
$\begin{align}
& 8.4=12k \\
& k=\frac{8.4}{12} \\
& k=\frac{7}{10}
\end{align}$
Substitute B = 56 and $k=\frac{7}{10}$ in $B\ =\ kD$.
$\begin{align}
& B=kD \\
& 56=\frac{7}{10}D \\
& D=\frac{56\times 10}{7} \\
& D=80
\end{align}$
Thus, if the ball is dropped from 80 inches, it bounces 56 inches.
