Solve for Proportions: Converting 1 Cup of Flour for 3 Cookies to 6 Cookies

To solve this problem, let's determine how many cups of flour are needed to make six cookies using proportions.

Initially, we know that 1 cup of flour produces 3 cookies. Our task is to determine how many cups ($x$) will be necessary for 6 cookies.

We can set up a proportion based on the information given:

$\frac{1}{3} = \frac{x}{6}$

To solve for $x$ (the unknown number of cups), we cross-multiply:

$(1 \times 6) = (3 \times x)$

This simplifies to:

$6 = 3x$

Next, divide both sides of the equation by 3 to isolate $x$:

$x = \frac{6}{3} = 2$

Therefore, 2 cups of flour are needed for six cookies.

The solution to the problem is 2 cups.