To determine how much butter Jennie needs when using 10 tablespoons of kernels, we first need to understand the ratio of butter to kernels in the original recipe.
The original recipe is:
- 1/2 cup of butter
- 3 tablespoons of kernels
Let's convert 1/2 cup of butter to tablespoons since the kernels are measured in tablespoons.
1 cup = 16 tablespoons, so: \[ \frac{1}{2} \text{ cup} = \frac{1}{2} \times 16 \text{ tablespoons} = 8 \text{ tablespoons} \]
Now, the ratio of butter to kernels in the original recipe is: \[ \text{Butter} : \text{Kernels} = 8 \text{ tablespoons} : 3 \text{ tablespoons} \]
Next, we find how much butter is needed when using 10 tablespoons of kernels. We can set up a proportion: \[ \frac{8 \text{ tablespoons of butter}}{3 \text{ tablespoons of kernels}} = \frac{x \text{ tablespoons of butter}}{10 \text{ tablespoons of kernels}} \]
Cross-multiplying gives us: \[ 8 \cdot 10 = 3 \cdot x \] \[ 80 = 3x \]
Now, solve for \(x\): \[ x = \frac{80}{3} \approx 26.67 \text{ tablespoons of butter} \]
To convert this back to cups: \[ \text{Cups of butter} = \frac{26.67}{16} \approx 1.66625 \text{ cups} \]
Rounding to the nearest hundredth gives us: \[ 1.67 \text{ cups} \]
Thus, the amount of butter Jennie needs when using 10 tablespoons of kernels is 1.67 cups.