Question

maxwells vegetarian tacos require \\(\frac{3}{4}\\) tablespoons of chili powder for every \\(\frac{1}{2}\\) pound of vegetables. how much chili powder will maxwell need if he uses \\(1\frac{3}{4}\\) pounds of vegetables?

\\(2\frac{1}{4}\\) tablespoons
\\(2\frac{1}{2}\\) tablespoons
\\(2\frac{5}{8}\\) tablespoons
\\(3\frac{1}{4}\\) tablespoons

Explanation:

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<reasoning>

Calculate the unit rate of chili powder per pound of vegetables

\[
\text{Unit Rate} = \frac{\frac{3}{4}\text{ tablespoons}}{\frac{1}{2}\text{ pound}} = \frac{3}{4} \times 2 = \frac{3}{2}\text{ tablespoons per pound}
\]

Calculate the total chili powder needed for the given amount of vegetables

\[

$$\begin{aligned} \text{Vegetables} &= 1\frac{3}{4}\text{ pounds} = \frac{7}{4}\text{ pounds} \\ \text{Chili Powder} &= \frac{3}{2} \times \frac{7}{4} = \frac{21}{8}\text{ tablespoons} \end{aligned}$$

\]

Convert the improper fraction to a mixed number

\[
\frac{21}{8} = 2\frac{5}{8}\text{ tablespoons}
\]
</reasoning>

<answer>
<mcq-option>(A) \(2\frac{1}{4}\) tablespoons</mcq-option>
<mcq-option>(B) \(2\frac{1}{2}\) tablespoons</mcq-option>
<mcq-correct>(C) \(2\frac{5}{8}\) tablespoons</mcq-correct>
<mcq-option>(D) \(3\frac{1}{4}\) tablespoons</mcq-option>
</answer>

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Answer:

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<reasoning>

Calculate the unit rate of chili powder per pound of vegetables

\[
\text{Unit Rate} = \frac{\frac{3}{4}\text{ tablespoons}}{\frac{1}{2}\text{ pound}} = \frac{3}{4} \times 2 = \frac{3}{2}\text{ tablespoons per pound}
\]

Calculate the total chili powder needed for the given amount of vegetables

\[

$$\begin{aligned} \text{Vegetables} &= 1\frac{3}{4}\text{ pounds} = \frac{7}{4}\text{ pounds} \\ \text{Chili Powder} &= \frac{3}{2} \times \frac{7}{4} = \frac{21}{8}\text{ tablespoons} \end{aligned}$$

\]

Convert the improper fraction to a mixed number

\[
\frac{21}{8} = 2\frac{5}{8}\text{ tablespoons}
\]
</reasoning>

<answer>
<mcq-option>(A) \(2\frac{1}{4}\) tablespoons</mcq-option>
<mcq-option>(B) \(2\frac{1}{2}\) tablespoons</mcq-option>
<mcq-correct>(C) \(2\frac{5}{8}\) tablespoons</mcq-correct>
<mcq-option>(D) \(3\frac{1}{4}\) tablespoons</mcq-option>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
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"Proportional Relationships"
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