Question

John and his friends but four bags of popcorn and three sodas at a movies for a total of $13.50 at the next movie John and his friends bought two bags of popcorn and 5 sodas for a total of $12 how much will John and his friends pay in dollars for 5 bags of popcorn and two sodas

Answer 1

To answer this question you will set up a system of equations to represent each scenario.  Solve for one variable and substitute that in to the other equation to find the missing value.  This example will have you solving for p, the price of popcorn.

4p + 3s = 13.50    and 2p + 5s = 12

2p + 5s = 12
      -2p    -2p
5s = 12 - 2p
5         5
s = 2.4 - 0.4p

4p + 3s = 13.50 
4p + 3(2.4 - 0.4p) = 13.50
4p +7.2 - 1.2p = 13.5
 2.8p +7.2 = 13.5
       -7.2       -7.2 
   2.8p = 6.3
   2.8      2.8
   p = 2.25

The price of popcorn is 2.25 and the soda is (2.4 - 0.4 x 2.25) $1.50.

5 popcorn and 2 sodas will cost (2.25 x 5 + 1.50 x 2) = $14.25.