Question

the drama club hosted a one act play competition. the given table shows the number of student tickets and the number of adult tickets that were sold each night, along with the total sales. write a system of equations that could be used to determine the price for a student ticket, \\(x\\), and the price for an adult ticket, \\(y\\).

\\(\

$$\begin{array}{|c|c|c|}\\hline & \\text{friday} & \\text{saturday} \\\\\\hline \\text{student tickets} & 40 & 30 \\\\\\hline \\text{adult tickets} & 50 & 45 \\\\\\hline \\text{total sales} & \\$615 & \\$525 \\\\\\hline\\end{array}$$

\\)

\\(\bigcirc\\) \\(\

$$\begin{aligned} 40x + 50y &= 615 \\\\ 30x + 45y &= 525 \\end{aligned}$$

\\)

\\(\bigcirc\\) \\(\

$$\begin{aligned} x + y &= 615 \\\\ x + y &= 525 \\end{aligned}$$

\\)

\\(\bigcirc\\) \\(\

$$\begin{aligned} 40x + 30y &= 70 \\\\ 50x + 45y &= 95 \\end{aligned}$$

\\)

\\(\bigcirc\\) \\(\

$$\begin{aligned} x + y &= 70 \\\\ x + y &= 95 \\end{aligned}$$

\\)

Explanation:

Define variables and Friday's sales equation

Using the Formulating Systems of Equations knowledge point

$$
LATEXBLOCK0
$$

Define Saturday's sales equation

Using the Formulating Systems of Equations knowledge point

$$ 30x + 45y = 525 $$

Combine into a system of equations

Using the Formulating Systems of Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

• **(A) \(

$$\begin{aligned} 40x + 50y &= 615 \\ 30x + 45y &= 525 \end{aligned}$$

\) (Correct answer)**

• (B) \(

$$\begin{aligned} x + y &= 615 \\ x + y &= 525 \end{aligned}$$

\)

• (C) \(

$$\begin{aligned} 40x + 30y &= 70 \\ 50x + 45y &= 95 \end{aligned}$$

\)

• (D) \(

$$\begin{aligned} x + y &= 70 \\ x + y &= 95 \end{aligned}$$

\)