To find out how many pounds of turnips Jasper bought, we first need to determine how much the turnips weigh based on the weight of the parsnips.
Jasper bought parsnips weighing 3 pounds. The turnips weigh \( 8 \frac{3}{4} \) times as much as the parsnips.
First, we convert \( 8 \frac{3}{4} \) to an improper fraction: \[ 8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \]
Now we can calculate the weight of the turnips: \[ \text{Weight of turnips} = 3 \times \frac{35}{4} = \frac{3 \times 35}{4} = \frac{105}{4} \]
Next, we convert this improper fraction into a mixed number: \[ \frac{105}{4} = 26 \frac{1}{4} \]
Therefore, the weight of the turnips that Jasper bought is: \[ \boxed{26 \frac{1}{4}} \text{ pounds} \]