An event coordinator is auditing the ticket sales for a local community fundraiser. They sold a total of 120 tickets. Student tickets ($s$) were priced at $5 each, and Adult tickets ($a$) were priced at $12 each. The total receipts for the event were $950. Match each description of the ticket sales data with its correct algebraic representation.

As an event coordinator reviewing the financial audit for a corporate charity movie night, you use a system of equations to verify ticket sales. You assign $a$ to represent the number of adult tickets sold for 11 dollars each and $c$ to represent the number of child tickets sold for 8 dollars each. In your audit calculations, you write the expression ${}11a + 8c$. What does this expression specifically represent in the context of this mixture application?

A cinema manager is training a new box office auditor to reconcile daily sales when the automated ticketing system reports a discrepancy. Suppose the theater sold 147 tickets for a total of 1,302 dollars, with adult tickets at 11 dollars and child tickets at 8 dollars. To determine the exact number of adult and child tickets sold using a system of equations, in what order should the auditor perform these steps?

Interpreting Ticket Sales Equations

When defining the variables for a movie theater ticket mixture application, the variables (such as $a$ and $c$) are used to represent the price of each ticket type.

Reconciling Theater Sales Using Systems of Equations

An assistant manager at a local cinema is reconciling the box office sales from the evening show. A total of 147 tickets were sold, and receipts totaled 1,302 dollars. To find how many adult tickets (priced at 11 dollars each) and child tickets (priced at 8 dollars each) were sold, the manager sets up the system of equations:

$a + c = 147$ ${}11a + 8c = 1302$

In this system, the coefficients 11 and 8 in the second equation represent the individual ____ of each respective ticket type.