Answer
20 pounds
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.
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Let F be the force, d the distance.
1.
$d$ varies directly as $F,\ \qquad d=kF$
2.
$9=k(12) \qquad /\div 12$
$\displaystyle \frac{9}{12}=k$
$k=\displaystyle \frac{3}{4}=0.75$
3.
$d=\displaystyle \frac{3}{4}F$
4.
$d=15,\ F=?$
$15=\displaystyle \frac{3}{4}F\qquad /\times\frac{4}{3}$
$F=\displaystyle \frac{15\cdot 4}{3}=20$ lb
