The original recipe calls for 3 tablespoons of kernels and 12 cups of butter.
To determine the amount of butter needed for 10 tablespoons of kernels, we can set up a proportion based on the original recipe.
Let \( x \) be the amount of butter needed for 10 tablespoons of kernels.
The proportion can be set up as follows:
\[ \frac{3 \text{ tablespoons of kernels}}{12 \text{ cups of butter}} = \frac{10 \text{ tablespoons of kernels}}{x \text{ cups of butter}} \]
Cross-multiplying gives us:
\[ 3x = 12 \times 10 \]
Calculating the right side:
\[ 3x = 120 \]
Now, divide both sides by 3 to solve for \( x \):
\[ x = \frac{120}{3} = 40 \]
Thus, Jennie needs 40 cups of butter when she uses 10 tablespoons of kernels.
In conclusion, the answer is:
\[ \boxed{40.00} \text{ cups of butter} \]