Question
2 cups hazelnuts (240g)
1/4 tsp pure vanilla extract
1/4 cup cocoa powder
1/3 cup sweetener of choice (see above for options that work here)
1/4 tsp salt
1/2 cup milk of choice or 2 tbsp oil, optional
This is a recipe for hazelnut spread, I have 2 and 3/4 cup hazelnuts what is the new ratio of the other ingredients?
Answers
Answered by
GPT-4o mini
To adjust the recipe for hazelnut spread based on having 2 and 3/4 cups (or 2.75 cups) of hazelnuts instead of the original 2 cups, we can calculate the ratios for each of the other ingredients.
First, let's determine the scaling factor:
\[
\text{Scaling Factor} = \frac{\text{New amount of hazelnuts}}{\text{Original amount of hazelnuts}} = \frac{2.75}{2} = 1.375
\]
Now, let's multiply each of the other ingredients by this scaling factor (1.375):
1. **Pure vanilla extract**:
\[
1/4 \, \text{tsp} \times 1.375 = \frac{1.375}{4} \text{tsp} = 0.34375 \text{tsp} \approx 1/3 \text{tsp or a little less}
\]
2. **Cocoa powder**:
\[
1/4 \, \text{cup} \times 1.375 = \frac{1.375}{4} \text{cup} = 0.34375 \text{cup} \approx 1/3 \text{cup} (a bit more than 1/3 cup)
\]
3. **Sweetener of choice**:
\[
1/3 \, \text{cup} \times 1.375 = \frac{1.375}{3} \text{cup} \approx 0.4583 \text{cup} \approx 1/2 \text{cup}
\]
4. **Salt**:
\[
1/4 \, \text{tsp} \times 1.375 = \frac{1.375}{4} \text{tsp} \approx 0.34375 \text{tsp} \approx 1/3 \text{tsp or a little less}
\]
5. **Milk or oil**:
\[
1/2 \, \text{cup} \times 1.375 = 0.6875 \text{cup} \approx 2/3 \text{cup}
\]
or if using oil:
\[
2 \, \text{tbsp} \times 1.375 = 2.75 \text{tbsp} \approx 2 \text{tbsp} + 2.25 \text{tsp}
\]
Here are the new proportions rounded for simplicity:
- **Hazelnuts**: 2.75 cups
- **Pure vanilla extract**: ~1/3 tsp
- **Cocoa powder**: ~1/3 cup (a bit more than 1/3 cup)
- **Sweetener**: ~1/2 cup
- **Salt**: ~1/3 tsp
- **Milk or oil**: ~2/3 cup or ~2.75 tbsp oil
These measurements should give you a balanced hazelnut spread based on your available hazelnuts!
First, let's determine the scaling factor:
\[
\text{Scaling Factor} = \frac{\text{New amount of hazelnuts}}{\text{Original amount of hazelnuts}} = \frac{2.75}{2} = 1.375
\]
Now, let's multiply each of the other ingredients by this scaling factor (1.375):
1. **Pure vanilla extract**:
\[
1/4 \, \text{tsp} \times 1.375 = \frac{1.375}{4} \text{tsp} = 0.34375 \text{tsp} \approx 1/3 \text{tsp or a little less}
\]
2. **Cocoa powder**:
\[
1/4 \, \text{cup} \times 1.375 = \frac{1.375}{4} \text{cup} = 0.34375 \text{cup} \approx 1/3 \text{cup} (a bit more than 1/3 cup)
\]
3. **Sweetener of choice**:
\[
1/3 \, \text{cup} \times 1.375 = \frac{1.375}{3} \text{cup} \approx 0.4583 \text{cup} \approx 1/2 \text{cup}
\]
4. **Salt**:
\[
1/4 \, \text{tsp} \times 1.375 = \frac{1.375}{4} \text{tsp} \approx 0.34375 \text{tsp} \approx 1/3 \text{tsp or a little less}
\]
5. **Milk or oil**:
\[
1/2 \, \text{cup} \times 1.375 = 0.6875 \text{cup} \approx 2/3 \text{cup}
\]
or if using oil:
\[
2 \, \text{tbsp} \times 1.375 = 2.75 \text{tbsp} \approx 2 \text{tbsp} + 2.25 \text{tsp}
\]
Here are the new proportions rounded for simplicity:
- **Hazelnuts**: 2.75 cups
- **Pure vanilla extract**: ~1/3 tsp
- **Cocoa powder**: ~1/3 cup (a bit more than 1/3 cup)
- **Sweetener**: ~1/2 cup
- **Salt**: ~1/3 tsp
- **Milk or oil**: ~2/3 cup or ~2.75 tbsp oil
These measurements should give you a balanced hazelnut spread based on your available hazelnuts!
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