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SOLUTION
From the question given, we are told that the demand D for bags, is inversely related to the price p. This is mathematically written as
[tex]\begin{gathered} D\propto\frac{1}{p} \\ \propto is\text{ a sign of proportionality. } \end{gathered}[/tex]If the proportionality sign is removed, a constant k will be introduced, and this becomes
[tex]D=\frac{k}{p}[/tex](A) We are told that when the price per bag is $3.25, demand is 144 bags.
Hence D = 144 and p = 3.25, now let's find k using the equation above
[tex]\begin{gathered} D=\frac{k}{p} \\ 144=\frac{k}{3.25} \\ k=144\times3.25 \\ k=468 \end{gathered}[/tex]Hence the equation that relates D to p is
[tex]D=\frac{468}{p}[/tex](B) If the price is raised to $4.00 per bag, the theater will sell?
Using the relationship, this becomes
[tex]\begin{gathered} D=\frac{468}{p} \\ D=\frac{468}{4.00} \\ D=117\text{ bags } \end{gathered}[/tex]Hence the answer is 117 bags.
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