Use the following number line to determine if expressions are true or false

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.