Question

3. Students performed in a play on a Friday and a Saturday. For bothperformances, adult tickets cost a dollars each and student tickets cost s dollarseach. 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, andcollect $1,230. This situation is represented by this system of equations below:125a + 65 = 1,200140a + 50s = 1,2303a. What could the equation 265a + 115s = 2,430 mean in this situation?*Your answer3b. The solution to the original system is the pair a=7 and s=5. Explain whyit makes sense that this pair of values is also the solution to the equation265a + 115s = 2,430.*

Answer 1

From the problem, we have the equation for the tickets sold on friday :

`125a+65s=1200`

and the equation for the tickets sold on saturday :

`140a+50s=1230`

3a. The equation 265a + 115s = 2430 is the total tickets sold on friday and saturday.

The answer is total tickets sold on friday and saturday

3b. a = 7 and s = 5

This pair is a solution to the equation because it is the cost of each ticket.

When substituting the values to the equation, the equation will be true.

`\begin{gathered} 265(7)+115(5)=2430 \\ 2430=2430 \\ \text{True} \end{gathered}`