Imagine you are the finance coordinator for a local community soccer tournament. You are reviewing a ticket sales report and need to verify the system of equations used to track the data. The tournament sold adult tickets ($x$) for ${}10$, student tickets ($y$) for ${}8$, and child tickets ($z$) for ${}5$. A total of ${}600$ tickets were sold, bringing in {}4{,}900 in total revenue. Additionally, the report shows that the number of adult tickets sold was exactly twice the number of child tickets sold. Match each part of the report's data to the linear equation that models it.

A community soccer club sells adult tickets ($x$) for ${}10$, student tickets ($y$) for ${}8$, and child tickets ($z$) for ${}5$. In the system of equations used to model their ticket sales, the total revenue is represented by the equation ${}10x + 8y + 5z = 4900$. What does the coefficient ${}8$ specifically represent in this equation?

As a box office manager for a local soccer tournament, you are reviewing the mathematical model used to track ticket sales. In this model, where $x$ represents the number of adult tickets sold and $z$ represents the number of child tickets sold, the equation $x - 2z = 0$ is used to represent the finding that the number of adult tickets sold was exactly twice the number of child tickets sold.

Identifying Variables in a Ticket Sales Model

As an event coordinator reconciling the box office report for a company-sponsored soccer tournament, you need to set up a mathematical model. Adult tickets ($x$) cost 10 dollars, student tickets ($y$) cost 8 dollars, and child tickets ($z$) cost 5 dollars. The report indicates a total of 600 tickets were sold across all categories. To represent the total number of tickets sold in your system of equations, you write the equation: $x + y + z =$ ____.

Modelling Ticket Sales for a Corporate Charity Match

Imagine you are an operations analyst reconciling ticket sales data for a community stadium's charity soccer match. You are using a system of three linear equations to find the exact number of adult tickets ($x$), student tickets ($y$), and child tickets ($z$) sold:

Equation 1: $x + y + z = 600$ Equation 2: ${}10x + 8y + 5z = 4900$ Equation 3: $x - 2z = 0$

Arrange the algebraic steps in the correct order to solve this system using the substitution method.