To find out how much butter Jennie needs when using 10 tablespoons of kernels, we first need to establish the ratio of kernels to butter based on the original recipe.
The original recipe calls for:
- 1/2 cup of butter
- 3 tablespoons of kernels
Since we need to adjust for 10 tablespoons of kernels, we can set up a proportion.
First, convert 1/2 cup of butter to tablespoons, as there are 8 tablespoons in 1 cup:
\[ 1/2 \text{ cup} = 4 \text{ tablespoons} \]
Now, we know that:
- 3 tablespoons of kernels requires 4 tablespoons of butter.
We need to find out how many tablespoons of butter correspond to 10 tablespoons of kernels. We can set up the proportion:
\[ \frac{3 \text{ tablespoons of kernels}}{4 \text{ tablespoons of butter}} = \frac{10 \text{ tablespoons of kernels}}{x \text{ tablespoons of butter}} \]
Cross-multiplying gives:
\[ 3x = 4 \times 10 \] \[ 3x = 40 \] \[ x = \frac{40}{3} \approx 13.33 \text{ tablespoons of butter} \]
Next, we convert this back into cups:
Since there are 8 tablespoons in a cup:
\[ \frac{13.33 \text{ tablespoons}}{8 \text{ tablespoons/cup}} \approx 1.66625 \text{ cups} \]
Rounding to the nearest hundredth, we get:
\[ 1.67 \text{ cups of butter} \]
Thus, the answer is:
1.67