To determine the number of cups of mix (sugar and flour) required to make 180 cookies, we can use the concept of ratios.
In the given recipe, the ratio of sugar to flour is 2 cups to 6 cups, which simplifies to 1:3. This means for every cup of sugar, there are 3 cups of flour.
To find the amount of mix required for 180 cookies, we need to determine how many sets of 1 cup of sugar and 3 cups of flour would be needed.
If the original recipe yields 60 cookies, we can calculate the ratio of cookies to the amount of mix required. It will be 60 cookies divided by (2 cups of sugar + 6 cups of flour), which is equivalent to 60 cookies divided by 8 cups of mix.
Therefore, the ratio of cookies to mix is 60 cookies : 8 cups of mix, which simplifies to 15 cookies : 2 cups of mix.
Now, we can determine how many sets of 15 cookies are needed to make 180 cookies. By setting up a proportion, we have:
15 cookies / 2 cups of mix = 180 cookies / x cups of mix
Cross-multiplying, we get:
15 cookies * x cups of mix = 2 cups of mix * 180 cookies
15x = 360
Dividing both sides by 15:
x = 24
Therefore, to make 180 cookies, you would need 24 cups of mix (sugar and flour combined).