A video store manager observes that the number of videos sold seems to vary inversely as the price per video. If the store sells 610 videos per week when the price per video is $\$ 15.70$, how many does he expect to sell if he lowers the price to $\$ 13.60$ ? Round your answer to the nearest integer if necessary.

Answer

Step 1 ：The problem describes an inverse variation. Inverse variation can be modeled by the equation \(y = k/x\), where \(k\) is the constant of variation. In this case, the number of videos sold (\(y\)) varies inversely with the price per video (\(x\)).

Step 2 ：We can find the constant of variation by plugging in the given values into the equation: \(610 = k/15.70\).

Step 3 ：Solving for \(k\), we get \(k = 9577.0\).

Step 4 ：We can use this constant of variation to predict the number of videos sold when the price is $13.60. We substitute \(k = 9577.0\) and \(x = 13.60\) into the equation \(y = k/x\).

Step 5 ：Solving for \(y\), we get \(y = 704\).

Step 6 ：Final Answer: The manager expects to sell \(\boxed{704}\) videos if he lowers the price to $13.60.