Sure! Let's break down the steps to determine which two recipes have equivalent ratios of cups of flour to the number of cookies:
1. Identify the given data:
- Peanut Butter: 3 cups of flour for 48 cookies.
- Oatmeal: 3 cups of flour for 27 cookies.
- Macadamia Nut: 2 cups of flour for 25 cookies.
- Sugar: 4 cups of flour for 64 cookies.
2. Calculate the ratio of cups of flour to the number of cookies for each recipe:
- Peanut Butter: [tex]\(\frac{3 \text{ cups}}{48 \text{ cookies}} = 0.0625\)[/tex]
- Oatmeal: [tex]\(\frac{3 \text{ cups}}{27 \text{ cookies}} = 0.1111\)[/tex]
- Macadamia Nut: [tex]\(\frac{2 \text{ cups}}{25 \text{ cookies}} = 0.08\)[/tex]
- Sugar: [tex]\(\frac{4 \text{ cups}}{64 \text{ cookies}} = 0.0625\)[/tex]
3. Compare the ratios to find equivalent ones:
- The Peanut Butter recipe ratio is [tex]\(0.0625\)[/tex].
- The Oatmeal recipe ratio is [tex]\(0.1111\)[/tex].
- The Macadamia Nut recipe ratio is [tex]\(0.08\)[/tex].
- The Sugar recipe ratio is [tex]\(0.0625\)[/tex].
4. Identify pairs with equivalent ratios:
- Comparing the ratios:
- Peanut Butter ratio is [tex]\(0.0625\)[/tex].
- Oatmeal ratio is [tex]\(0.1111\)[/tex].
- Macadamia Nut ratio is [tex]\(0.08\)[/tex].
- Sugar ratio is [tex]\(0.0625\)[/tex].
- The recipes Peanut Butter and Sugar both have a ratio of [tex]\(0.0625\)[/tex], meaning their ratios are equivalent.
5. Conclusion:
The two recipes that have equivalent ratios of cups of flour to the number of cookies are:
- Peanut Butter and Sugar.
So, the final answer is:
Peanut Butter and Sugar recipes have equivalent ratios of cups of flour to the number of cookies.
