6. The total revenue of a magic show is \( 16,360 \mathrm{EGP} \). If each adult ticket to nttend the show cost 12 EGP and each children ticket cost 2 EGP , then what is the number of tickets of each type sold if 3,480 tickets in all were sold? A. 930 adult tickets and 2,550 children tickets B. 940 adult tickets and 2,540 children tickets C. 955 adult tickets and 2,525 children tickets D. 960 adult tickets and 2,520 children tickets

To solve this problem, we need to establish a system of equations based on the information provided. Let’s denote the number of adult tickets as \( x \) and the number of children tickets as \( y \). From the problem, we have two equations: 1. The total number of tickets sold: \( x + y = 3,480 \) 2. The total revenue generated: \( 12x + 2y = 16,360 \) Now, let's isolate \( y \) from the first equation: \( y = 3,480 - x \) Substituting \( y \) in the second equation gives: \( 12x + 2(3,480 - x) = 16,360 \) Simplifying, we find: \( 12x + 6,960 - 2x = 16,360 \) This leads to: \( 10x = 9,400 \) Thus, \( x = 940 \). So, the number of adult tickets sold is \( 940 \), and substituting back to find \( y \): \( y = 3,480 - 940 = 2,540 \). So, the answer is **B. 940 adult tickets and 2,540 children tickets**. Dealing with ticket sales has a long history, especially in entertainment! From the ancient Roman amphitheaters that charged for entry to modern-day concerts, calculating ticket sales involves understanding audience demographics and appropriate pricing strategies to maximize revenue. When tackling such problems, make sure to double-check your equations and calculations. A common mistake is misreading the total revenue or number of tickets sold, which can lead to incorrect conclusions. Always verify your numbers with practical context—like ensuring that the adult ticket price aligns with typical prices in similar events!