To determine how much butter Jennie needs when using 10 tablespoons of kernels, we first need to establish the ratio of butter to kernels based on the original recipe.
The original recipe calls for:
- Butter: \( \frac{1}{2} \) cup
- Kernels: 3 tablespoons
Now, we can set up a proportion based on these amounts.
Let \( x \) be the amount of butter needed for 10 tablespoons of kernels:
\[ \frac{\frac{1}{2} \text{ cup}}{3 \text{ tablespoons}} = \frac{x \text{ cups}}{10 \text{ tablespoons}} \]
Cross-multiplying gives:
\[ \frac{1}{2} \text{ cup} \times 10 = 3 \text{ tablespoons} \times x \text{ cups} \]
This simplifies to:
\[ 5 = 3x \]
Now, solving for \( x \):
\[ x = \frac{5}{3} \]
Calculating \( \frac{5}{3} \):
\[ \frac{5}{3} \approx 1.6667 \]
Rounding this to the nearest hundredth gives:
\[ 1.67 \]
So, the answer is:
1.67