Question

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

a \\( 2 \frac{1}{4} \\) tablespoons
b \\( 2 \frac{1}{2} \\) tablespoons
c \\( 2 \frac{5}{8} \\) tablespoons
d \\( 3 \frac{1}{4} \\) tablespoons

Explanation:

Step1: Convert mixed numbers to fractions

First, convert the given mixed numbers to improper fractions:

• $\frac{3}{4}$ tablespoon (chili powder per $\frac{1}{2}$ lb veggies) stays as $\frac{3}{4}$
• $1\frac{3}{4}$ pounds of veggies = $\frac{1\times4 + 3}{4} = \frac{7}{4}$ pounds
• $\frac{1}{2}$ pounds of veggies = $\frac{1}{2}$ pounds

Step2: Find scaling factor

Calculate how many times the base amount of veggies is used:
$\text{Scaling factor} = \frac{\text{Total veggies}}{\text{Base veggies}} = \frac{\frac{7}{4}}{\frac{1}{2}} = \frac{7}{4} \times \frac{2}{1} = \frac{7}{2}$

Step3: Calculate total chili powder

Multiply the base chili powder by the scaling factor:
$\text{Total chili powder} = \frac{3}{4} \times \frac{7}{2} = \frac{21}{8}$

Step4: Convert back to mixed number

Convert $\frac{21}{8}$ to a mixed number:
$\frac{21}{8} = 2\frac{5}{8}$

Answer:

C. $2\frac{5}{8}$ tablespoons