Business: Theater Attendance The manager of the Coral...

Business: Theater Attendance The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. One day in July, 5200 tickets were sold and the receipts totaled $\$ 29,961 .$ The adult admission is $\$ 7.50,$ and the children's admission is $\$ 4.50 .$ How many adult patrons were there?

Business: Theater Attendance The manager of the Coral Theater wants to know whether the majority of its patrons
are adults or children. One day in July, 5200 tickets were sold and the receipts totaled $\$ 29,961 .$ The adult admission is
$\$ 7.50,$ and the children's admission is $\$ 4.50 .$ How many adult patrons were there?

Key Concepts

Systems of Linear Equations

Systems of linear equations consist of multiple equations that model relationships between variables, which are solved simultaneously. In a context like ticket sales, one equation can represent the total number of tickets sold while another represents the total revenue, allowing for a determination of individual ticket types through their interrelated values.

Algebraic Modeling

Algebraic modeling is the process of translating real-world situations into mathematical expressions by defining variables and constructing equations based on given data. This is essential in scenarios like theater attendance, where ticket counts and pricing information are converted into a system of equations that can be solved to reveal underlying quantities.

Substitution Method

The substitution method is a strategy used to solve systems of equations by expressing one variable in terms of another using one equation and then substituting this expression into the other equation. This method simplifies the problem and is particularly useful when one equation can be easily rearranged to isolate a variable.

Revenue Analysis

Revenue analysis involves examining the income generated from different sources, such as distinct ticket prices for adults and children. By incorporating pricing data into algebraic models, businesses can determine the contributions of various segments to the overall revenue, aiding in profitability and attendance assessments.

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