Question

four plumbers each charge a flat fee plus an hourly rate for repair visits. the table shows their total costs for repairs that required various amounts of time.

which plumber charges the greatest hourly rate?

plumber a
plumber b
plumber c
plumber d

Explanation:

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<reasoning>

Understand the linear cost model

The total cost for each plumber is represented by a linear function:
\[\text{Total Cost} = \text{Flat Fee} + (\text{Hourly Rate} \times \text{Hours})\]
The hourly rate is the Rate of Change (or slope) of this Linear Functions model. We can calculate this rate by finding the change in cost per hour:
\[\text{Hourly Rate} = \frac{\text{Change in Cost}}{\text{Change in Hours}}\]

Calculate the hourly rate for Plumber A

Using the values for 1 hour (\$35) and 2 hours (\$65):
\[\text{Rate}_A = \frac{65 - 35}{2 - 1} = 30 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber B

Using the values for 1 hour (\$55) and 2 hours (\$75):
\[\text{Rate}_B = \frac{75 - 55}{2 - 1} = 20 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber C

Using the values for 1 hour (\$50) and 2 hours (\$75):
\[\text{Rate}_C = \frac{75 - 50}{2 - 1} = 25 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber D

Using the values for 1 hour (\$50) and 2 hours (\$60):
\[\text{Rate}_D = \frac{60 - 50}{2 - 1} = 10 \text{ dollars per hour}\]

Comparing the rates, Plumber A has the greatest hourly rate of \$30 per hour.
</reasoning>

<answer>
<mcq-correct>plumber A</mcq-correct>
<mcq-option>plumber B</mcq-option>
<mcq-option>plumber C</mcq-option>
<mcq-option>plumber D</mcq-option>
</answer>

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Answer:

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<reasoning>

Understand the linear cost model

The total cost for each plumber is represented by a linear function:
\[\text{Total Cost} = \text{Flat Fee} + (\text{Hourly Rate} \times \text{Hours})\]
The hourly rate is the Rate of Change (or slope) of this Linear Functions model. We can calculate this rate by finding the change in cost per hour:
\[\text{Hourly Rate} = \frac{\text{Change in Cost}}{\text{Change in Hours}}\]

Calculate the hourly rate for Plumber A

Using the values for 1 hour (\$35) and 2 hours (\$65):
\[\text{Rate}_A = \frac{65 - 35}{2 - 1} = 30 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber B

Using the values for 1 hour (\$55) and 2 hours (\$75):
\[\text{Rate}_B = \frac{75 - 55}{2 - 1} = 20 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber C

Using the values for 1 hour (\$50) and 2 hours (\$75):
\[\text{Rate}_C = \frac{75 - 50}{2 - 1} = 25 \text{ dollars per hour}\]

Calculate the hourly rate for Plumber D

Using the values for 1 hour (\$50) and 2 hours (\$60):
\[\text{Rate}_D = \frac{60 - 50}{2 - 1} = 10 \text{ dollars per hour}\]

Comparing the rates, Plumber A has the greatest hourly rate of \$30 per hour.
</reasoning>

<answer>
<mcq-correct>plumber A</mcq-correct>
<mcq-option>plumber B</mcq-option>
<mcq-option>plumber C</mcq-option>
<mcq-option>plumber D</mcq-option>
</answer>

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