To determine how much butter Jennie needs when using 10 tablespoons of kernels instead of the original 3 tablespoons, we can set up a ratio based on the original recipe.
-
Original recipe:
- Butter: \( \frac{1}{2} \) cup
- Kernels: 3 tablespoons
-
New amount of kernels: 10 tablespoons
We can find the scaling factor by dividing the new amount of kernels by the original amount of kernels:
\[ \text{Scaling factor} = \frac{10 \text{ tablespoons}}{3 \text{ tablespoons}} = \frac{10}{3} \approx 3.3333 \]
Now, we apply this scaling factor to the amount of butter:
\[ \text{Butter needed} = \left(\frac{1}{2} \text{ cup}\right) \times \left(\frac{10}{3}\right) \]
First, we need to convert \( \frac{1}{2} \) cup to tablespoons since we are working with tablespoons for kernels. There are 16 tablespoons in a cup, so:
\[ \frac{1}{2} \text{ cup} = 8 \text{ tablespoons} \]
Now we can calculate the amount of butter needed:
\[ \text{Butter needed} = 8 \text{ tablespoons} \times \frac{10}{3} \]
Now calculate:
\[ = \frac{80}{3} \text{ tablespoons} \approx 26.6667 \text{ tablespoons} \]
To convert this back to cups, we divide by 16 (since there are 16 tablespoons in a cup):
\[ \text{Butter in cups} = \frac{26.6667}{16} \approx 1.6667 \text{ cups} \]
To round to the nearest hundredth, we get:
\[ \text{Butter needed} \approx 1.67 \text{ cups} \]
Thus, Jennie needs approximately 1.67 cups of butter when using 10 tablespoons of kernels.