Final answer:
Using a proportion based on the given recipe ratio, it is determined that 1/4 cup of milk is needed for 1 cup of chocolate syrup.
Step-by-step explanation:
The student has asked how many cups of milk are used for 1 cup of chocolate syrup if a chocolate milk recipe takes a mixture of 1/6 cup of milk to 2/3 cup of chocolate syrup. To find the number of cups of milk needed for 1 cup of chocolate syrup, we create a proportion based on the recipe's ratio.
According to the given recipe ratio:
1/6 cup of milk / 2/3 cup of chocolate syrup = x cups of milk / 1 cup of chocolate syrup
By solving for x, we get:
x = (1/6) * (1 / (2/3))
x = (1/6) * (3/2)
x = 1/4
Therefore, 1/4 cup of milk is used for 1 cup of chocolate syrup.