Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels, how much butter does she need? round to the nearest hundredth.

To determine how much butter Jennie needs when she uses 10 tablespoons of kernels instead of 3 tablespoons, we'll first find the ratio of kernels and butter in the recipe.

The original recipe requires:
- 1/2 cup of butter
- 3 tablespoons of kernels

Let's convert 1/2 cup of butter to tablespoons because the quantity of kernels is in tablespoons.

1 cup = 16 tablespoons, therefore:
\[
\frac{1}{2} \text{ cup} = 8 \text{ tablespoons}
\]

Now we have:
- Butter: 8 tablespoons
- Kernels: 3 tablespoons

Next, we'll find the ratio of butter to kernels:
\[
\text{Ratio} = \frac{8 \text{ tablespoons of butter}}{3 \text{ tablespoons of kernels}} \approx 2.67 \text{ tablespoons of butter per tablespoon of kernels}
\]

Now, if Jennie uses 10 tablespoons of kernels, we can calculate the amount of butter she needs by multiplying the number of kernels by this ratio:
\[
\text{Butter needed} = 10 \text{ tablespoons of kernels} \times \frac{8 \text{ tablespoons of butter}}{3 \text{ tablespoons of kernels}} = \frac{80 \text{ tablespoons of butter}}{3} \approx 26.67 \text{ tablespoons of butter}
\]

Now we need to convert the quantity of butter back into cups:
\[
\text{Butter in cups} = \frac{26.67 \text{ tablespoons}}{16 \text{ tablespoons per cup}} \approx 1.67 \text{ cups}
\]

So, rounding to the nearest hundredth, the amount of butter needed is approximately:
\[
\text{Butter needed} \approx 1.67
\]

The correct answer is **c. 1.67**.