- Understand that the number of tablespoons \(T\) is proportional to the number of cups \(C\) by the equation \(T = 16 \times C\).
- Test each given table by multiplying the number of cups by \(16\) to see if it results in the number of tablespoons listed.
- Table 1 satisfies the equation \(T = 16 \times C\) for all pairs: \(16(1)=16\), \(16(2)=32\), \(16(4)=64\), and \(16(8)=128\).
- The correct table is:
\[ \begin{array}{|l|l|} \ \text{cups} & \text{tablespoons} \\ 1 & 16 \\ 2 & 32 \\ 4 & 64 \\ 8 & 128 \\ \end{array} \]
Explanation
- Analyzing the Relationship between Cups and Tablespoons
The problem establishes a relationship between the number of cups (\(C\)) and the number of tablespoons (\(T\)). It states that \(1\) cup is equivalent to \(16\) tablespoons. This relationship can be expressed as a linear function where the number of tablespoons is directly proportional to the number of cups: \(T = 16 \times C\). Our goal is to identify which of the three given tables satisfies this equation for all provided pairs of values.
- Evaluating the Given Tables
We will test the formula \(T = 16 \times C\) against the pairs in each table.
Table 1:
- For \(C = 1\), \(T = 16 \times 1 = 16\). (Matches)
- For \(C = 2\), \(T = 16 \times 2 = 32\). (Matches)
- For \(C = 4\), \(T = 16 \times 4 = 64\). (Matches)
- For \(C = 8\), \(T = 16 \times 8 = 128\). (Matches)
Table 2:
- For \(C = 16\), the formula predicts \(T = 16 \times 16 = 256\), but the table lists \(T = 1\). (Does not match)
Table 3:
- For \(C = 32\), the formula predicts \(T = 16 \times 32 = 512\), but the table lists \(T = 16\). (Does not match)
Since only Table 1 satisfies the relationship \(T = 16 \times C\) for all provided values, it is the correct table.
- Conclusion
Based on the analysis, Table 1 correctly relates the number of cups to the number of tablespoons according to the rule \(T = 16 \times C\). The final answer is the first table.
Examples
In cooking, precise measurements are essential for a recipe to turn out perfectly. Knowing how units like cups and tablespoons relate allows you to scale recipes up or down. If a recipe calls for half a cup and you only have a tablespoon measure, understanding that \(0.5 \text{ cups} \times 16 \text{ tablespoons/cup} = 8 \text{ tablespoons}\) helps you measure ingredients accurately, ensuring your dish is seasoned and balanced just right.