a) Variables
• d: distance a person is from the pivot, in ft
,
• w: person's weight, in lbs
Since the variables are inversely proportional, then they are related by the next formula:
[tex]d=\frac{k}{w}[/tex]
where k is constant.
b) Where w = 145 lbs, d = 6 ft. Substituting these values into the previous formula and solving for k:
[tex]\begin{gathered} 6=\frac{k}{145} \\ 6\cdot145=\frac{k}{145}\cdot145 \\ 870=k \end{gathered}[/tex]
Substituting into the formula with d = 5 ft and k = 870, and solving for w, we get:
[tex]\begin{gathered} 5=\frac{870}{w} \\ 5\cdot\frac{w}{5}=\frac{870}{w}\cdot\frac{w}{5} \\ w=174\text{ lbs} \end{gathered}[/tex]
c) Substituting into the formula with w = 87 lbs and k = 870, and solving for d, we get:
[tex]\begin{gathered} d=\frac{870}{87} \\ d=10\text{ ft} \end{gathered}[/tex]
