As you saw in "Paying the Plumber," we can use a system of equations to model real-world situations.

It worked because we had:

- Two equations
- Both equations used the same two variables (x represented hours and y represented cost)

We can try to represent other situations using a system of equations.

For example, imagine you owned a movie theater. On Saturday, you played the movie, "Knowing" with Nicholas Cage. Adult tickets cost $8 per person and children's tickets cost $6 per person. You sold a total of 280 tickets and had total ticket sales of $2120. How many of each type of ticket (adult, child) did you selll?

To solve:

- Choose meaningful variables to represent the items that you do not know their actual value.

A - the number of Adult tickets, C - the number of childrens' tickets. - Write two equations. Each equation must use both of the variables above.

Total number of tickets sold:*A*+*C*= 280

Total ticket sales:**8**($8 for each adult ticket and $6 for each child's)*A*+ 6*C*= $2120 - Solve using Linear Combinations or Substitution.
- Check your answer using Dooley's System Solver. For this system the solution is (220, 60).
- Describe what your solution means. In this system, I sold 220 Adult's tickets and 60 children's tickets.

Activity 2: Decisions, Decisions, Decisions

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Using Systems of Equations to model a Situation