Maxwell's vegetarian tacos require [tex]\frac{3}{4}[/tex] tablespoons of chili powder for every [tex]\frac{1}{2}[/tex] pound of vegetables. How much chili powder will Maxwell need if he uses [tex]1 \frac{3}{4}[/tex] pounds of vegetables?

A. [tex]2 \frac{1}{4}[/tex] tablespoons
B. [tex]2 \frac{1}{2}[/tex] tablespoons
C. [tex]2 \frac{5}{8}[/tex] tablespoons
D. [tex]3 \frac{1}{4}[/tex] tablespoons

We start by finding the amount of chili powder per pound of vegetables. Maxwell's recipe calls for

[tex]$$
\frac{3}{4} \text{ tablespoon of chili powder for } \frac{1}{2} \text{ pound of vegetables.}
$$[/tex]

To find the rate per one pound, we compute

[tex]$$
\text{Rate} = \frac{\frac{3}{4}}{\frac{1}{2}} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4} = \frac{6}{4} = \frac{3}{2} \text{ tablespoons per pound}.
$$[/tex]

Next, Maxwell uses [tex]$1\frac{3}{4}$[/tex] pounds of vegetables. First, convert this to an improper fraction:

[tex]$$
1\frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ pounds.}
$$[/tex]

Now, multiply the weight of the vegetables by the rate of chili powder per pound:

[tex]$$
\text{Chili powder needed} = \frac{3}{2} \times \frac{7}{4} = \frac{21}{8} \text{ tablespoons.}
$$[/tex]

To express [tex]$\frac{21}{8}$[/tex] as a mixed number, note that

[tex]$$
\frac{21}{8} = 2\frac{5}{8}
$$[/tex]

since [tex]$2$[/tex] whole parts equal [tex]$\frac{16}{8}$[/tex] and there are [tex]$\frac{5}{8}$[/tex] remaining.

Thus, Maxwell needs

[tex]$$
2\frac{5}{8} \text{ tablespoons of chili powder.}
$$[/tex]