Originally Posted by

**Jhevon** here's how i interpret the problem. how many videos should a nonmember buy to make having a membership worthwhile in the first place. if say we were just going to rent one video and never rent from that store again, then it doesn't make sense to have a membership, since we would end up spending $22.50 to get the video with membership instead of just $3 without the membership. the same holds for 2, videos, and 3 and so on. we want to find how many videos we must rent so that becoming a member would end up cheaper.

first let's find where the member and the nonmember spends the same amount of money.

Let v be the number of videos rented.

a nonmember will spend 3v dollars, since he pays $3 for each video.

a member would pay 1.5v dollars, since he would pay $1.50 for each video, PLUS the membership fee of $21. so equating these two we get:

3v = 1.5v + 21

=> 3v - 1.5v = 21 ..........get the v's on one side by subtracting 1.5v from both sides

=> 1.5v = 21 .................calculate the left hand side

=> v = 21/1.5 ...............divide both sides by 1.5

=> v = 14

So at the 14th video rented, the member and non member pays the same amount of money in total. if we rent any more videos than this, it would be cheaper to be a member, since we would pay $1.50 for each additional video above 14, as opposed to $3 for each video above 14 if we are nonmembers.

So renting more than 14 videos justifies the membership