Answer
about 607 lb
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 w be the weight (pounds), h the height (inches).
1.
$w$ varies directly as $h^{3},\ \qquad w=kh^{3}$
2.
$170=k(70^{3}) $
$170=k(343,000) \qquad /\div 343,000$
$\displaystyle \frac{170}{343,000}=k$
$ k\approx$0.0004956
3.
$w=$0.0004956$h^{3}$
4.
$h=107, w=?$
$w=$0.0004956$(107^{3})\approx$607.164169096
about 607 lb
