Question

jason has applied to be a camp counselor for the summer. the job pays \\$9 per hour. the equation to represent jasons job is \\(y = 9x\\), where \\(x\\) is the number of hours he works and \\(y\\) is the total amount he earns.

mia has applied to be a lifeguard for the summer. the lifeguard job is three days a week with hours and pay as shown in the table below.

\

$$\begin{tabular}{|l|c|c|c|} \\hline & tuesday & thursday & saturday \\\\ \\hline hours worked & 6 & 8 & 5 \\\\ \\hline amount paid & \\$52.50 & \\$70.00 & \\$43.75 \\\\ \\hline \\end{tabular}$$

which statement best describes the hourly rates?

• the two jobs pay the same hourly rate.
• the comparison cannot be made with the information given.
• jasons camp counselor job pays a higher hourly rate than mias lifeguard job.
• jasons camp counselor job pays a lower hourly rate than mias lifeguard job.

Explanation:

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</pre_analysis>

<reasoning>

Identify Jason's hourly rate

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &y = 9x\\ &\text{Hourly rate} = \$9\text{ per hour} \end{aligned}$$

\]

Calculate Mia's hourly rate

Using the Representing Proportional Relationships in Tables and Constant of Proportionality knowledge points
\[

$$\begin{aligned} &\text{Tuesday: } \frac{\$52.50}{6} = \$8.75\text{ per hour}\\ &\text{Thursday: } \frac{\$70.00}{8} = \$8.75\text{ per hour}\\ &\text{Saturday: } \frac{\$43.75}{5} = \$8.75\text{ per hour} \end{aligned}$$

\]

Compare the hourly rates

We compare the two calculated unit rates to determine which job pays more.

• Jason's hourly rate: \(\$9.00\) per hour
• Mia's hourly rate: \(\$8.75\) per hour

Since \(\$9.00 > \$8.75\), Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.
</reasoning>

<answer>
<mcq-option>The two jobs pay the same hourly rate.</mcq-option>
<mcq-option>The comparison cannot be made with the information given.</mcq-option>
<mcq-correct>Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.</mcq-correct>
<mcq-option>Jason's camp counselor job pays a lower hourly rate than Mia's lifeguard job.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Unit Rate Comparison"
]
}
</post_analysis>

Answer:

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<reasoning>

Identify Jason's hourly rate

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &y = 9x\\ &\text{Hourly rate} = \$9\text{ per hour} \end{aligned}$$

\]

Calculate Mia's hourly rate

Using the Representing Proportional Relationships in Tables and Constant of Proportionality knowledge points
\[

$$\begin{aligned} &\text{Tuesday: } \frac{\$52.50}{6} = \$8.75\text{ per hour}\\ &\text{Thursday: } \frac{\$70.00}{8} = \$8.75\text{ per hour}\\ &\text{Saturday: } \frac{\$43.75}{5} = \$8.75\text{ per hour} \end{aligned}$$

\]

Compare the hourly rates

We compare the two calculated unit rates to determine which job pays more.

• Jason's hourly rate: \(\$9.00\) per hour
• Mia's hourly rate: \(\$8.75\) per hour

Since \(\$9.00 > \$8.75\), Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.
</reasoning>

<answer>
<mcq-option>The two jobs pay the same hourly rate.</mcq-option>
<mcq-option>The comparison cannot be made with the information given.</mcq-option>
<mcq-correct>Jason's camp counselor job pays a higher hourly rate than Mia's lifeguard job.</mcq-correct>
<mcq-option>Jason's camp counselor job pays a lower hourly rate than Mia's lifeguard job.</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
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"Unit Rate Comparison"
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