Final answer:
To find out how many cups of sugar Trina needs for 3 cups of flour, we use proportions. Since the original recipe uses z cups of sugar for 7 cups of flour, the proportion for 3 cups of flour would be less than half of z. Based on the available options and the process of elimination, 2 cups of sugar is the most plausible answer.
Step-by-step explanation:
The question asks how many cups of sugar Trina would need if she uses 3 cups of flour. To solve this, we need to create a proportional relationship between the amounts of sugar and flour used in the recipe. Originally, she uses z cups of sugar for 7 cups of flour.
Setting up a proportion, we have:
z cups sugar / 7 cups flour = x cups sugar / 3 cups flour
Now, solve for x:
7x = 3z
x = (3z) / 7
We don't know the exact value of z, but we are looking for a proportional relationship. Since the flour is reduced to less than half (from 7 to 3 cups), the sugar will also be less than half. Therefore, the correct proportional amount cannot be more than half of z.
The available options are:
- A) 2 cups
- B) 3 cups
- C) 21 cups
- D) 7 cups
Option C is not possible because it's 3 times more than the original amount of z, and Option D is the original amount of sugar, not a proportional decrease. Between Options A and B, since Option A is the one that represents less than half of z, it is the most plausible answer without knowing the exact value of z — assuming z is at least 4 or more.