Final answer:
The amount of brown sugar used per cup of white sugar based on the given recipe proportions, a cross multiplication is performed resulting in 8/9 cups of brown sugar per 1 cup of white sugar, which is not listed in the provided answer choices.
Step-by-step explanation:
To find out how much brown sugar is used per cup of white sugar in the given recipe, we follow a simple proportion calculation. First, we set up our proportion with the given amounts: 3/4 cups of brown sugar for each 2/3 cups of white sugar. We are interested in finding out the equivalent amount per one cup of white sugar. Let's represent the unknown amount of brown sugar as 'x'.
The proportion we'll set up is:
¾ cups brown sugar / ¾ cups white sugar = x cups brown sugar / 1 cup white sugar
Cross-multiplying gives us:
(3/4) * 1 = (2/3) * x
This simplifies to:
3/4 = 2x/3
Now, to solve for 'x', we will cross-multiply:
3 * x = 4 * (2/3)
x = 8/9
Thus, the answer is 8/9 cups of brown sugar per 1 cup of white sugar. None of the provided answer choices (A. 1 1/8 cups, B. 7/12 cups, C. 1 1/4 cups, D. 4/5 cups) match our calculated result.