Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.

Sagot :

xero099

The solution of the system of linear equations is [tex]x = 50[/tex], [tex]y = 20[/tex].

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]

To learn more on systems of linear equations, we kindly invite to check this verified question: https://brainly.com/question/20379472

View image xero099
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.