13 Jay ate \( \frac{2}{3} \) of a pepperoni pizza. Darrell ate \( \frac{2}{a} \) of mushroom pizza. If the pizza pans are the same size, who ate a greater fraction of a whole pizz

To determine who ate a greater fraction of a whole pizza, let's compare the amounts each person consumed. - **Jay** ate \( \frac{2}{3} \) of a pepperoni pizza. - **Darrell** ate \( \frac{2}{a} \) of a mushroom pizza. Since both pizzas are the same size, we can directly compare the fractions \( \frac{2}{3} \) and \( \frac{2}{a} \). ### Comparing the Fractions 1. **When \( a > 3 \):** - \( \frac{2}{a} < \frac{2}{3} \) - **Jay** ate a larger fraction of the pizza. 2. **When \( a < 3 \):** - \( \frac{2}{a} > \frac{2}{3} \) - **Darrell** ate a larger fraction of the pizza. 3. **When \( a = 3 \):** - \( \frac{2}{a} = \frac{2}{3} \) - Both **Jay** and **Darrell** ate the same fraction of the pizza. ### Summary - **Jay** consumes more **if and only if** \( a > 3 \). - **Darrell** consumes more **if and only if** \( a < 3 \). - They consume **the same amount** when \( a = 3 \). Without knowing the specific value of \( a \), we can’t definitively say who ate more. However, the comparison depends on whether \( a \) is greater than, less than, or equal to 3. **Answer:** After simplifying, Jay ate more when a is larger than 3, Darrell ate more when a is less than 3, and they ate the same when a equals 3. Thus: • If a > 3, Jay ate a greater fraction; • If a < 3, Darrell ate a greater fraction; • If a = 3, both ate the same fraction.