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Lesson: 3.5 Variation and Multivariable Fu...
MADELIN SCOTT
Question 6 of 7 , Step 1 of 1
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A video store manager observes that the number of DVDs sold seems to vary inversely as the price per DVD. If the store sells 440 DVDs per week when the price per DVD is $\mathrm{\$}16.60$, how many does he expect to sell if he lowers the price to $\mathrm{\$}15.10$ ? Round your answer to the nearest integer if necessary.
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Step 1 ：Given that the number of DVDs sold varies inversely with the price per DVD, we can use the formula for inverse variation: $y=\frac{k}{x}$, where $y$ is the number of DVDs sold, $x$ is the price per DVD, and $k$ is the constant of variation.

Step 2 ：Using the initial conditions, where 440 DVDs are sold at a price of $16.60, we can find the constant of variation $k$ by rearranging the formula: $k=y\cdot x$.

Step 3 ：Substitute the given values into the equation to find $k$: $k=440\cdot 16.60$.

Step 4 ：Calculate the value of $k$: $k=7304$.

Step 5 ：Now, to find the expected number of DVDs sold at the new price of $15.10, we use the same formula: $y=\frac{k}{x}$.

Step 6 ：Substitute the value of $k$ and the new price into the equation to find $y$: $y=\frac{7304}{15.10}$.

Step 7 ：Calculate the expected number of DVDs sold: $y=484$.

Step 8 ：Round the answer to the nearest integer if necessary, which in this case, it is not.

Step 9 ：The final answer is $\boxed{{\displaystyle 484}}$