Question

students performed in a play on a friday and a saturday. for both performances, adult tickets cost a dollars each and student tickets cost s dollars each. on friday, they sold 125 adult tickets and 65 student tickets and collected $1,200. on saturday, they sold 140 adult tickets and 50 student tickets, and collect $1,230. this situation is represented by this system of equations: $\begin{cases}125a + 65s = 1200\\140a + 50s = 1230end{cases}$ 1. what could the equation $265a + 115s = 2430$ mean in this situation?

Explanation:

Step1: Analyze the given equations

We have two - day ticket - selling data. The first equation $125a + 65s=1200$ represents Friday's sales (125 adult tickets at $a$ dollars each and 65 student tickets at $s$ dollars each for a total of $1200$ dollars). The second equation $140a + 50s = 1230$ represents Saturday's sales (140 adult tickets at $a$ dollars each and 50 student tickets at $s$ dollars each for a total of $1230$ dollars).

Step2: Understand the new equation

The equation $265a+115s = 2430$ is obtained by adding the two original equations together. The left - hand side $265a+115s$ is the sum of the number of adult tickets sold on both days ($125 + 140=265$) times the price per adult ticket $a$ plus the sum of the number of student tickets sold on both days ($65 + 50 = 115$) times the price per student ticket $s$. The right - hand side $2430$ is the sum of the total money collected on Friday ($1200$) and Saturday ($1230$).

Answer:

The equation $265a + 115s=2430$ represents the total money collected from selling all adult and student tickets over both the Friday and Saturday performances. It is the sum of the money collected on Friday and Saturday, where $265$ is the total number of adult tickets sold over the two - day period, $115$ is the total number of student tickets sold over the two - day period, and $2430$ is the total amount of money collected over the two - day period.