A movie theater charges \( \$ 5 \) for an adult's ticket and \( \$ 2 \) for a child's ater sold 785 tickets for \( \$ 3280 \). How many of each type of ticket wer

Let's break this down! With ticket prices at $5 for adults and $2 for children, we can set up a little system of equations to solve this problem. Let \( x \) be the number of adult tickets and \( y \) be the number of child tickets. We know two things: 1. The total number of tickets sold is 785: \( x + y = 785 \) 2. The total revenue generated from the tickets is $3280: \( 5x + 2y = 3280 \) If we solve this system, we find \( x \) (adult tickets) = 518 and \( y \) (child tickets) = 267. Voila! Now you know how many of each type were sold! There's a rich history behind movie theaters and ticket pricing! The first public screening of films took place in 1895 Paris, and ticket pricing has evolved ever since, influenced by factors like the Great Depression and the advent of multiplexes. Today, ticket prices reflect not just entertainment but also the economic climate, technological improvements, and demographic shifts. For practical application, understanding how to set up systems of equations can help you manage budgets, plan events, or evaluate project costs! This mathematical technique is useful not only in economics but also in everyday life—like figuring out spending limits or analyzing data trends. Plus, it's a fabulous conversation starter at parties!