Bot GPT 4-o mini To determine how much butter Jennie needs when using 10 tablespoons of kernels, we first need to find the ratio of butter to kernels in the original recipe and then apply that ratio to the new amount of kernels.
The original recipe calls for:
- 1/2 cup of butter
- 3 tablespoons of kernels
First, let's convert the butter amount into tablespoons, because the kernel measurement is given in tablespoons.
1 cup = 16 tablespoons, so: \[ \frac{1}{2} \text{ cup of butter} = \frac{1}{2} \times 16 = 8 \text{ tablespoons of butter} \]
Next, we have the original ratio of butter to kernels:
- Butter: 8 tablespoons
- Kernels: 3 tablespoons
Now, calculate the ratio of butter per tablespoon of kernels: \[ \text{Butter per kernel} = \frac{8 \text{ tablespoons of butter}}{3 \text{ tablespoons of kernels}} \approx 2.6667 \text{ tablespoons of butter per tablespoon of kernels} \]
Now apply this ratio to find out how much butter is needed for 10 tablespoons of kernels: \[ \text{Butter needed} = 10 \text{ tablespoons of kernels} \times 2.6667 \text{ tablespoons of butter per tablespoon of kernels} \approx 26.6667 \text{ tablespoons of butter} \]
Finally, convert back to cups: \[ 26.6667 \text{ tablespoons of butter} = \frac{26.6667}{16} \text{ cups} \approx 1.6667 \text{ cups} \]
Therefore, rounding to the nearest hundredth, the amount of butter needed is approximately: \[ \text{Butter needed} \approx 1.67 \text{ cups} \]
So, if Jennie uses 10 tablespoons of kernels, she needs approximately 1.67 cups of butter.
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