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 \\(\

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

\\)

h \\(\

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

\\)

g \\(\

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

\\)

j \\(\

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

\\)

Explanation:

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<reasoning>

Define variables and total seats

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

$$\begin{aligned} &c = \text{number of regular chairs}\\ &s = \text{number of 3-legged stools}\\ &c + s = 9 \end{aligned}$$

\]

Model total number of legs

Using the Linear Function Modeling knowledge point
\[

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

\]

Formulate the system of equations

Using the Systems of Linear Equations knowledge point
\[

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

\]

Analyze incorrect option F

Using the Systems of Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Option F states: } c + s = 33 \text{ and } 4c + 3s = 9\\ &\text{This incorrectly equates total seats } (c+s) \text{ to total legs } (33)\\ &\text{And incorrectly equates total legs } (4c+3s) \text{ to total seats } (9) \end{aligned}$$

\]
</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 Systems of Linear Equations and Linear Function Modeling knowledge points
\[

$$\begin{aligned} &c = \text{number of regular chairs}\\ &s = \text{number of 3-legged stools}\\ &c + s = 9 \end{aligned}$$

\]

Model total number of legs

Using the Linear Function Modeling knowledge point
\[

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

\]

Formulate the system of equations

Using the Systems of Linear Equations knowledge point
\[

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

\]

Analyze incorrect option F

Using the Systems of Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Option F states: } c + s = 33 \text{ and } 4c + 3s = 9\\ &\text{This incorrectly equates total seats } (c+s) \text{ to total legs } (33)\\ &\text{And incorrectly equates total legs } (4c+3s) \text{ to total seats } (9) \end{aligned}$$

\]
</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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