A cookie recipe calls for 3 cups of sugar and yields 24 cookies. How many cups of sugar will be needed to make 3 dozen cookies? Express your answer as a mixed number in lowest terms.

To determine how many cups of sugar are needed to make 3 dozen cookies, we first need to convert dozens to individual cookies. 1 dozen = 12 cookies, so 3 dozen = 3 × 12 = 36 cookies. The original recipe yields 24 cookies using 3 cups of sugar. We can find the amount of sugar needed per cookie: \[ \text{Sugar per cookie} = \frac{3 \text{ cups}}{24 \text{ cookies}} = \frac{1}{8} \text{ cup per cookie} \] Next, we calculate the amount of sugar needed for 36 cookies: \[ \text{Sugar for 36 cookies} = 36 \text{ cookies} \times \frac{1}{8} \text{ cup per cookie} = \frac{36}{8} \text{ cups} \] Now, we simplify \(\frac{36}{8}\): \[ \frac{36}{8} = \frac{9}{2} \text{ cups} \] To express \(\frac{9}{2}\) as a mixed number: \[ \frac{9}{2} = 4 \frac{1}{2} \] Thus, the amount of sugar needed to make 3 dozen cookies is \[ \boxed{4 \frac{1}{2}} \text{ cups}. \]