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Sagot :
In the question, we are given that demand is inversely related to the price. We can find the solution to the required questions below;
Explanation
An inverse relationship is one in which the value of one parameter tends to decrease as the value of the other parameter in the relationship increases. It is often described as a negative relationship.
Using letters that are peculiar to the given quantities we can get their relationship to be;
[tex]\begin{gathered} d\propto\frac{1}{p} \\ \therefore d=\frac{k}{p}\text{ where k is the constant of proportionality} \end{gathered}[/tex]Part A
For part A, when the price of candy is $3.00 per bag and the theater sells 182 bags of candy. We can substitute the values into the above expression to get the demand for candy in terms of price.
[tex]\begin{gathered} 182=\frac{k}{3} \\ \therefore k=546 \\ \text{Then, we substitute the value of k back in the formula } \\ d=\frac{546}{p} \end{gathered}[/tex]Answer:
[tex]d=\frac{546}{p}[/tex]Part B
We can determine the number of bags of candy that will be sold if the price is raised to $3.25 a bag below.
Using the initial relationship gotten from part A we would have;
[tex]\begin{gathered} d=\frac{546}{3.25} \\ d=168 \end{gathered}[/tex]Therefore, the answer is;
Answer: 168
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