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 ticke

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.