To determine how much butter Jennie needs for 10 tablespoons of kernels, we first need to establish the ratio of kernels to butter in the original recipe.
The original recipe uses:
- 1/2 cup of butter
- 3 tablespoons of kernels
First, we convert the butter measurement to tablespoons, knowing that 1 cup = 16 tablespoons:
1/2 cup of butter = 8 tablespoons
The ratio of butter to kernels in the original recipe is:
\[ \text{Butter} : \text{Kernels} = 8 \text{ tablespoons} : 3 \text{ tablespoons} \]
To find out how much butter is needed for 10 tablespoons of kernels, we set up a proportion based on the original ratio:
\[ \frac{8 \text{ tablespoons of butter}}{3 \text{ tablespoons of kernels}} = \frac{x \text{ tablespoons of butter}}{10 \text{ tablespoons of kernels}} \]
Cross-multiplying gives us:
\[ 8 \times 10 = 3 \times x \]
So,
\[ 80 = 3x \]
Now, we solve for \(x\):
\[ x = \frac{80}{3} \approx 26.67 \text{ tablespoons of butter} \]
To convert this back to cups, we divide by 16 (since there are 16 tablespoons in a cup):
\[ \text{Butter in cups} = \frac{26.67}{16} \approx 1.6667 \text{ cups} \]
Rounding to the nearest hundredth gives:
\[ \text{Butter needed} \approx 1.67 \text{ cups} \]
Thus, the answer is 1.67.
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