To determine the amount of flour needed to make 144 cookies, we can follow these detailed steps:
1. Identify the amount of flour for the given recipe:
- The recipe states it uses [tex]\(3 \frac{1}{4}\)[/tex] cups of flour per batch.
- Converting the mixed number to a decimal gives [tex]\(3.25\)[/tex] cups of flour.
2. Identify how many cookies the recipe makes:
- The recipe yields 3 dozen cookies.
- Since 1 dozen equals 12 cookies, 3 dozen is [tex]\(3 \times 12 = 36\)[/tex] cookies.
3. Determine the flour needed for one cookie:
- To find the amount of flour needed for one cookie, divide the total cups of flour by the number of cookies the recipe makes.
[tex]\[
\text{Flour per cookie} = \frac{3.25 \text{ cups of flour}}{36 \text{ cookies}} = 0.09027777777777778 \text{ cups per cookie}
\][/tex]
4. Calculate the total amount of flour needed for 144 cookies:
- Multiply the amount of flour needed per cookie by the number of desired cookies.
[tex]\[
\text{Total flour needed} = 0.09027777777777778 \text{ cups per cookie} \times 144 \text{ cookies} = 13.0 \text{ cups of flour}
\][/tex]
Hence, you will need 13 cups of flour to make 144 cookies.
