Answer
80 in
Work Step by Step
Solving Variation Problems (see p. 424)
1. $\ \ $Write an equation that models the given English statement.
2. $\ \ $Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation.
3. $\ \ $Substitute the value of k into the equation in step 1.
4. $\ \ $Use the equation from step 3 to answer the problem's question.
-----------
1.
$B$ varies directly as $D,\ \qquad B=kD$
2.
$8.4=k(12) \qquad /\div 12$
$\displaystyle \frac{8.4}{12}=k$
$k=0.7$
3.
$B=0.7D$
4.
B=56, $D=?$
$56=0.7D\qquad /\div 0.7$
$D=\displaystyle \frac{56}{0.7}=\frac{560}{7}=80$ in
