Question

for spring cleanups, a landscaper charges a flat fee of \\$60 plus \\$20 for each hour of labor. which equation models the cost in dollars, \\(c\\), for a cleanup that requires \\(h\\) hours of labor?

\\(c = \frac{h}{20} + 60\\)

\\(c = \frac{20}{h} + 60\\)

\\(c = 20h + 60\\)

\\(c = 20 + 60h\\)

Explanation:

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<reasoning>

Identify the rate of change and initial value

\[

$$\begin{aligned} &\text{Rate of change (cost per hour of labor)} = 20\\ &\text{Initial value (flat fee)} = 60 \end{aligned}$$

\]

Formulate the linear equation

\[
c = 20h + 60
\]
</reasoning>

<answer>
<mcq-option>(A) \(c = \frac{h}{20} + 60\)</mcq-option>
<mcq-option>(B) \(c = \frac{20}{h} + 60\)</mcq-option>
<mcq-correct>(C) \(c = 20h + 60\)</mcq-correct>
<mcq-option>(D) \(c = 20 + 60h\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the rate of change and initial value

\[

$$\begin{aligned} &\text{Rate of change (cost per hour of labor)} = 20\\ &\text{Initial value (flat fee)} = 60 \end{aligned}$$

\]

Formulate the linear equation

\[
c = 20h + 60
\]
</reasoning>

<answer>
<mcq-option>(A) \(c = \frac{h}{20} + 60\)</mcq-option>
<mcq-option>(B) \(c = \frac{20}{h} + 60\)</mcq-option>
<mcq-correct>(C) \(c = 20h + 60\)</mcq-correct>
<mcq-option>(D) \(c = 20 + 60h\)</mcq-option>
</answer>

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