How much does each cost

Question

A local movie theater sells 4 tickets and 2 boxes of popcorn for $42, It also sells 6 movie tickets and 4 boxes of popcorn for $67.50. What are the prices for a single movie and a single popcorn.

Answer 1

Let p = the cost of a single box of popcorn

Let m = the cost of a single movie

 

4m + 2p = 42   divide this entire equation by 2: 2m + p = 21

6m + 4p = 67.50

2m + p = 21     Multiply this equation by -3: -6m - 3p = -63

Add the following equations together:

6m + 4p = 67.50

-6m - 3p = -63

            p = $4.50

 

2m + p = 21     Substitute 4.50 into this equation for p.

2m + 4.50 = 21

2m = 16.50      Divide by two.

   m = $8.25