To find the constant of proportionality, we need to identify the relationship between cups of tofu and cups of Sichuan chilis. The constant of proportionality is typically represented as the ratio of one quantity to another, denoted as \( k \) in the relationship \( y = kx \).
Based on your table, you have the following relationships involving cups of tofu (T) and cups of Sichuan chilis (S):
- \( 5 \cdot ? = 4 \)
- \( \frac{4}{5} = ? \)
- \( \frac{4}{1} \div 5 = ? \)
- \( 4 \cdot \frac{1}{5} = 20 \cdot 1 = ? \)
Let's compute the required values step by step:
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For \( 5 \cdot ? = 4 \): \[ ? = \frac{4}{5} \]
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For \( \frac{4}{5} = ? \): \[ ? = \frac{4}{5} \]
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For \( \frac{4}{1} \div 5 = ? \): \[ ? = \frac{4}{5} \]
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For \( 4 \cdot \frac{1}{5} = 20 \cdot 1 = ? \): This seems to be a miscalculation, as \( 4 \cdot \frac{1}{5} = \frac{4}{5} \) not \( 20 \cdot 1 \). The correct evaluation is: \[ 4 \cdot \frac{1}{5} = \frac{4}{5} \]
So, throughout the calculations, you can see that the constant of proportionality is consistently \( \frac{4}{5} \) when you relate cups of tofu to cups of Sichuan chilis.
The final answer can be summarized as:
- Constant of proportionality \( k = \frac{4}{5} \)
Here is the filled summary for the table:
| Cups of Tofu | Cups of Sichuan Chilis | Calculated Value | |---------------|------------------------|-----------------------------------| | 5 | \( \frac{4}{5} \) | \( ? = \frac{4}{5} \) | | 4 | | \( \frac{4}{5} = ? \) | | 4 | | \( \frac{4}{5} = ? \) | | 4 | | \( 4 \cdot \frac{1}{5} = \frac{4}{5} \) |
Let me know if you need any further assistance!