To determine if the three recipes use a proportional amount of flour, we need to compare the ratios of cookies to flour for each recipe.

Step 1: Express the ratio for each recipe

• Recipe 1: $\frac{\text{1 dozen cookies}}{\text{1 cup of flour}} = \frac{1}{1}$
• Recipe 2: $\frac{\text{3 dozen cookies}}{\text{3.5 cups of flour}} = \frac{3}{3.5} = \frac{30}{35} = \frac{6}{7}$
• Recipe 3: $\frac{\text{5 dozen cookies}}{\text{6 cups of flour}} = \frac{5}{6}$

Step 2: Compare the ratios

The ratios are:

• Recipe 1: $1$
• Recipe 2: $\frac{6}{7}$
• Recipe 3: $\frac{5}{6}$

Since the ratios are not equal, the three recipes do not use a proportional amount of flour.

Final Answer:

The three recipes do not use a proportional amount of flour.

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Related Questions:

1. How do you calculate a unit rate for these recipes (e.g., flour per cookie)?
2. What is the definition of proportional relationships in mathematics?
3. Can the ratios of these recipes be adjusted to make them proportional?
4. How can scaling the recipes help in finding proportionality?
5. What practical applications does proportionality have in baking and cooking?

Tip:

When comparing proportional relationships, always reduce the ratios to their simplest forms for easier comparison.