SOLUTION: A video store manager observes that the number of videos sold seems to vary inversely as the price per video. If the store sells 570 videos per week when the price per video is $17

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Question 1153213: A video store manager observes that the number of videos sold seems to vary inversely as the price per video. If the store sells 570 videos per week when the price per video is $17.40, how many does he expect to sell if he lowers the price to $13.10? Round your answer to two decimal places if necessary.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = constant of proportionality
Let +n+ = videos per week sold at lower price
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+570+=+k%2A%28+1%2F17.4+%29+
+k+=+570+%2F+17.4+
+k+=+32.76+
-------------------------
+n+=+k%2A%28+1%2F13.1+%29+
+n+=+32.76%2A%28+1%2F13.1+%29+
+n+=+2.5+
2.5 videos per week
In whole numbers, 5 videos every 2 weeks
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get a 2nd opinion if needed

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A video store manager observes that the number of videos sold seems to vary inversely as the price per video. If the store sells 570 videos per week when the price per video is $17.40, how many does he expect to sell if he lowers the price to $13.10? Round your answer to two decimal places if necessary.
Can't Josmiceli see that his answer makes NO SENSE?

What sense does it make for the manager to lower the price if sales are going to be reduced from 570 videos per week to 2.5 videos per week? Does this make any SENSE at all? 

Plus, isn't the reason behind INVERSE VARIATION, that when one increases the other decreases or vice versa?



Anyway, let number of videos be V, constant of proportionality, k, and price, P

We then get: 

matrix%281%2C3%2C+V%2C+%22=%22%2C+k%2FP%29

highlight_green%28matrix%281%2C3%2C+V%2C+%22=%22%2C+17.4%28570%29%2F13.1%29%29 ------ Substituting 17.4(570) for k, and 13.1 for P