human
If a particular recipe requires 3 cups of flour to yield 2 dozen cookies, how much flour would be necessary to prepare a batch of 6 dozen cookies, considering the proportionality of the ingredients?
gpt
Step 1: Determine the relationship between the number of cookies and the amount of flour.
In the given problem, 3 cups of flour are needed to make 2 dozen cookies.

Step 2: Set up a proportion to find the amount of flour needed for 6 dozen cookies.
Let x be the amount of flour needed for 6 dozen cookies. We can set up the proportion as follows:

(3 cups of flour) / (2 dozen cookies) = (x cups of flour) / (6 dozen cookies)

Step 3: Solve the proportion for x.
To solve the proportion, we can cross-multiply:

3 * 6 = 2 * x

Step 4: Simplify the equation.
18 = 2x

Step 5: Solve for x.
x = 18 / 2
x = 9

So, 9 cups of flour would be necessary to prepare a batch of 6 dozen cookies.