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.
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