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:

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<reasoning>

Define variables and Friday's sales equation

Using the Formulating Systems of Equations knowledge point
\[

$$\begin{aligned} &\text{Let } x = \text{price of a student ticket} \\ &\text{Let } y = \text{price of an adult ticket} \\ &40x + 50y = 615 \end{aligned}$$

\]

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
\[

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

\]
</reasoning>

<answer>
<mcq-correct>(A) \(

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

\)</mcq-correct>
<mcq-option>(B) \(

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

\)</mcq-option>
<mcq-option>(C) \(

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

\)</mcq-option>
<mcq-option>(D) \(

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

\)</mcq-option>
</answer>

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]
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</post_analysis>

Answer:

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<reasoning>

Define variables and Friday's sales equation

Using the Formulating Systems of Equations knowledge point
\[

$$\begin{aligned} &\text{Let } x = \text{price of a student ticket} \\ &\text{Let } y = \text{price of an adult ticket} \\ &40x + 50y = 615 \end{aligned}$$

\]

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
\[

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

\]
</reasoning>

<answer>
<mcq-correct>(A) \(

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

\)</mcq-correct>
<mcq-option>(B) \(

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

\)</mcq-option>
<mcq-option>(C) \(

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

\)</mcq-option>
<mcq-option>(D) \(

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

\)</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Formulating Systems of Equations"
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