Jennie is making popcorn. The recipe calls for 1/2

To determine how much butter Jennie needs when using 10 tablespoons of kernels instead of the original 3 tablespoons, we can set up a ratio based on the original recipe.

1. **Original recipe**:
- Butter: \( \frac{1}{2} \) cup
- Kernels: 3 tablespoons

2. **New amount of kernels**: 10 tablespoons

We can find the scaling factor by dividing the new amount of kernels by the original amount of kernels:

\[
\text{Scaling factor} = \frac{10 \text{ tablespoons}}{3 \text{ tablespoons}} = \frac{10}{3} \approx 3.3333
\]

Now, we apply this scaling factor to the amount of butter:

\[
\text{Butter needed} = \left(\frac{1}{2} \text{ cup}\right) \times \left(\frac{10}{3}\right)
\]

First, we need to convert \( \frac{1}{2} \) cup to tablespoons since we are working with tablespoons for kernels. There are 16 tablespoons in a cup, so:

\[
\frac{1}{2} \text{ cup} = 8 \text{ tablespoons}
\]

Now we can calculate the amount of butter needed:

\[
\text{Butter needed} = 8 \text{ tablespoons} \times \frac{10}{3}
\]

Now calculate:

\[
= \frac{80}{3} \text{ tablespoons} \approx 26.6667 \text{ tablespoons}
\]

To convert this back to cups, we divide by 16 (since there are 16 tablespoons in a cup):

\[
\text{Butter in cups} = \frac{26.6667}{16} \approx 1.6667 \text{ cups}
\]

To round to the nearest hundredth, we get:

\[
\text{Butter needed} \approx 1.67 \text{ cups}
\]

Thus, Jennie needs approximately **1.67 cups of butter** when using 10 tablespoons of kernels.