On a family outing, Tyler bought 5 cups of hot cocoa and 4 pretzels for $18.40. Some of his family members would like a second serving, so he went back to the same food stand and bought another 2
cups of hot cocoa and 4 pretzels for $11.20.
Here is a system of equations that represent the quantities and constraints in this situation.
5c + 4p = 18.40
2c + 4p = 11.20
1. What does the solution to the system, (c, p), represent in this situation?
2. If we add the second equation to the first equation, we have a new equation: 7c+ 8p = 29.60.
Explain why the same (c, p) pair that is a solution to the two original equations is also a solution to
this new equation.