Precalculus world problem

Question

During a one-month promotional campaign, Fran's Fix gave either a free DVD rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. In all 63 new members were signed up and the store's cost for the incentives was $108. How many of each incentive were given away?

Answer 1

r + p = 63

r + 2p = 108

We can solve this a few ways, but since I see just r in both equations, I am going to solve each equation for r.

r = 63 - p

r = 108 - 2p

Now, since r has 2 "values", those values are equal.

63 - p = 108 - 2p

p = 45 boxes of popcorn

r = 63 - 45

r = 18 free rentals