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