15.2: Concert Tickets 1. Tickets to a family concert cost \( \$ 10 \) for adults and \( \$ 3 \) for children. The concert organizers collected a total of \( \$ 900 \) from ticket sales. a. In this situation, what is the meaning of each variable in the equation \( 10 A+3 C=900 \) ? b. If 42 adults were at the concert, how many children attended? d. Write an equation to represent \( C \) as a function of \( A \). Explain what this funct tells us about the situation.

In the equation \( 10 A + 3 C = 900 \), \( A \) represents the number of adults attending the concert, while \( C \) represents the number of children. The coefficients (10 and 3) indicate the ticket prices for adults and children, respectively, and the total sum ($900) represents the total revenue generated from ticket sales. If 42 adults attended the concert, we can solve for the number of children by substituting \( A = 42 \) into the equation. This gives us \( 10(42) + 3C = 900 \), simplifying to \( 420 + 3C = 900 \). Solving for \( C \), we find that \( 3C = 480 \), leading to \( C = 160 \). Therefore, 160 children attended the concert. To express \( C \) as a function of \( A \), we can rearrange the equation to isolate \( C \): \( C = \frac{900 - 10A}{3} \). This function tells us how many children can attend based on the number of adults. As more adults attend, the number of children decreases in a predictable way, showing the balance between adult and child ticket sales!