A local children's theater sold tickets for their evening show at $5 for children and $15 for adults. For their afternoon matinee, the price was reduced to $2 for children and $5 for adults. They sold $550 worth of tickets for the evening show and $200 for the matinee.

Solve the system algebraically, and compare it with the graph you created. Explain the intersection point of the two equations in terms of the context.

The point of intersection represents the solution found analytically and represents the scenario in which the same quantity of adults and children assisted to both shows.

Procedure - Determination of the number of people assisting to a movie

Construction of the system of equations

In this question we need to construct a linear function for the total of people that assisted to the evening show and for the total of people that assisted to the afternoon matinee. The system of equations is described below:

Evening show

[tex]5\cdot x + 15\cdot y = 550[/tex] (1)

Afternoon matinee

[tex]2\cdot x + 5\cdot y = 200[/tex] (2)

Where:

[tex]x[/tex] - Number of children that assisted.
[tex]y[/tex] - Number of adults that assisted.

Resolution of the system of equations and analysis of the results

By algebraic means we find the following result associated with the system of equations:

[tex]x = 50[/tex], [tex]y = 20[/tex] [tex]\blacksquare[/tex]

The graphic representation of this system is described in the image attached below.

The point of intersection represents the solution found analytically and represents the scenario in which the same quantity of adults and children assisted to both shows. [tex]\blacksquare[/tex]

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