To create a table that shows the relationship between the number of cups of chocolate chips and the corresponding cups of pecans based on the given recipe, we need to set up the rate at which chocolate chips relate to pecans.
Given in the recipe:
- \( \frac{5}{4} \) cup of chocolate chips corresponds to \( \frac{7}{1} \) cup of pecans.
We need to find out how many cups of pecans are needed for 1 cup of chocolate chips.
First, we convert the relationship into a simpler form:
\[ \frac{5/4 \text{ cups of chocolate chips}}{7 \text{ cups of pecans}} \]
To find out how many cups of pecans correspond to 1 cup of chocolate chips, we can set up a proportion. Let \( x \) be the number of cups of pecans needed for 1 cup of chocolate chips:
\[ \frac{5/4}{7} = \frac{1}{x} \]
To solve for \( x \), we can cross-multiply:
\[ 5/4 \cdot x = 7 \cdot 1 \] \[ 5x = 28 \] \[ x = \frac{28}{5} \] \[ x = 5.6 \]
Now we can fill in a table for various amounts of chocolate chips (adding a few more than just 1 cup for context):
| Chocolate Chips (cups) | Pecans (cups) | |------------------------|----------------| | 0 | 0 | | 1 | 5.6 | | 2 | 11.2 | | 3 | 16.8 | | 4 | 22.4 |
Thus, to make trail mix with 1 cup of chocolate chips, you will need 5.6 cups of pecans.
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