Solving a Zoo Ticket Mixture Application

Solving a Movie Theater Ticket Mixture Application

As a staff member at a Science Center, you are tasked with auditing the weekend sales to find exactly how many adult and child tickets were sold. When using the system of equations method to solve this mixture problem, in what order should the following steps be performed?

A Science Center auditor is reviewing the revenue from a weekend event. If the number of adult tickets sold is $a$ and the number of child tickets sold is $c$, the total revenue is modeled by the equation ${}12a + 7c = 12{,}146$. What does the number 12 represent in this equation?

As a Science Center operations manager, you are verifying the algebraic setup used in your weekend sales audit. The center sold 1,363 tickets for a total revenue of 12,146 dollars. Adult tickets cost 12 dollars and child tickets cost 7 dollars. Let $a$ represent the number of adult tickets and $c$ represent the number of child tickets. Match each business metric to its corresponding mathematical representation.

As an operations manager at a Science Center, you are reviewing a system of equations used to audit weekend sales. If the equation $a + c = 1{,}363$ represents the total quantity of tickets sold, then the equation ${}12a + 7c = 12{,}146$ represents the total ____ collected from those sales.

As an auditor reviewing a science center's weekend ticket sales, you model the scenario with a system of equations where $a + c = 1{,}363$ represents the total quantity of tickets sold, and ${}12a + 7c = 12{,}146$ represents the total revenue. True or False: To solve this system using the elimination method, a correct procedural step is to multiply the entire first equation by $-7$ in order to eliminate the variable $c$.