Question

2 aaliyah has regular chairs and 3-legged stools for a party. she has 9 seats all together which makes up 33 legs. which system of equations can be used to find the number of regular chairs, \\(c\\), and the number of stools, \\(s\\), she has?

f \\(\

$$\begin{aligned} c + s &= 33 \\\\ 4c + 3s &= 9 \\end{aligned}$$

\\)

g \\(\

$$\begin{aligned} c + s &= 9 \\\\ 4c + 3s &= 33 \\end{aligned}$$

\\)

h \\(\

$$\begin{aligned} c + s &= 33 \\\\ 4s + 3c &= 9 \\end{aligned}$$

\\)

j \\(\

$$\begin{aligned} c + s &= 9 \\\\ 4s + 3c &= 33 \\end{aligned}$$

\\)

Explanation:

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<reasoning>

Define variables and total seats

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &c = \text{number of regular chairs}\\ &s = \text{number of stools}\\ &c + s = 9 \end{aligned}$$

\]

Model the total number of legs

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &\text{Legs per regular chair} = 4\\ &\text{Legs per stool} = 3\\ &4c + 3s = 33 \end{aligned}$$

\]

Formulate the system of equations

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{cases} c + s = 9 \\ 4c + 3s = 33 \end{cases}$$

\]

Analyze the incorrect option F

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &\text{Option F system:} \quad c + s = 33, \quad 4c + 3s = 9\\ &\text{Error 1: } c + s = 33 \text{ incorrectly equates total seats to 33 instead of 9.}\\ &\text{Error 2: } 4c + 3s = 9 \text{ incorrectly equates total legs to 9 instead of 33.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>F \(

$$\begin{cases} c + s = 33 \\ 4c + 3s = 9 \end{cases}$$

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

$$\begin{cases} c + s = 9 \\ 4c + 3s = 33 \end{cases}$$

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

$$\begin{cases} c + s = 33 \\ 4s + 3c = 9 \end{cases}$$

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

$$\begin{cases} c + s = 9 \\ 4s + 3c = 33 \end{cases}$$

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

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Answer:

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<reasoning>

Define variables and total seats

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &c = \text{number of regular chairs}\\ &s = \text{number of stools}\\ &c + s = 9 \end{aligned}$$

\]

Model the total number of legs

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &\text{Legs per regular chair} = 4\\ &\text{Legs per stool} = 3\\ &4c + 3s = 33 \end{aligned}$$

\]

Formulate the system of equations

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{cases} c + s = 9 \\ 4c + 3s = 33 \end{cases}$$

\]

Analyze the incorrect option F

Using the Linear Function Modeling and Linear Equations knowledge points
\[

$$\begin{aligned} &\text{Option F system:} \quad c + s = 33, \quad 4c + 3s = 9\\ &\text{Error 1: } c + s = 33 \text{ incorrectly equates total seats to 33 instead of 9.}\\ &\text{Error 2: } 4c + 3s = 9 \text{ incorrectly equates total legs to 9 instead of 33.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>F \(

$$\begin{cases} c + s = 33 \\ 4c + 3s = 9 \end{cases}$$

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

$$\begin{cases} c + s = 9 \\ 4c + 3s = 33 \end{cases}$$

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

$$\begin{cases} c + s = 33 \\ 4s + 3c = 9 \end{cases}$$

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

$$\begin{cases} c + s = 9 \\ 4s + 3c = 33 \end{cases}$$

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

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