From the question, we are told that a recipe needs 3/4 cup of sugar to make 24 cookies, this can be written as;
3/4 cups of sugar = 24 cookies
To get the amount of sugar needed to make 36 cookies, you will say;
x cups of sugar = 36 cookies
Equate both expressions;
3/4 cups of sugar = 24 cookies
x cups of sugar = 36 cookies
Cross multiply;
24 * x = 3/4 * 36
24x = 108/4
cross multiply;
24x * 4 = 108
96x = 108
x = 108/96
x = 1 12/96
x = 1 1/8
Hence 1 1/8 cups of sugar will be needed to make 36 cookies. Option C is correct