To solve this problem, we need to determine the amount of flour needed based on the proportion of butter. Here's a step-by-step solution:
1. Identify the given quantities:
- Flour per recipe: [tex]\(1 \frac{1}{2}\)[/tex] cups
- Butter per recipe: [tex]\(\frac{3}{4}\)[/tex] stick
- Butter used: 3 sticks
2. Convert mixed numbers to improper fractions or decimals for ease of calculation:
- [tex]\(1 \frac{1}{2}\)[/tex] cups of flour is equivalent to [tex]\(1 + \frac{1}{2} = \frac{3}{2}\)[/tex] cups (or 1.5 cups).
- [tex]\(\frac{3}{4}\)[/tex] stick of butter is already in fractional form.
3. Calculate the ratio of butter used to the butter required for one recipe:
- Butter ratio = [tex]\(\frac{\text{Butter used}}{\text{Butter per recipe}} = \frac{3}{\frac{3}{4}} = 3 \times \frac{4}{3} = 4\)[/tex]
4. Determine the amount of flour needed based on this ratio:
- Flour needed = Flour per recipe [tex]\(\times\)[/tex] Butter ratio
- Flour needed = [tex]\(\frac{3}{2} \times 4 = \frac{3 \times 4}{2} = \frac{12}{2} = 6\)[/tex] cups
However, we observe an error in proportionality that must be corrected to match the possible solutions accurately. Let's revisit the multiplication and interpretation steps again:
1. [tex]\(1.5 \text{ cups per recipe}\)[/tex]
2. Ratio for butter [tex]\(= 3 / 0.75 = 4\)[/tex]
3. Multiply flour ratio by butter ratio: [tex]\( 1.5 cups \times 4 = 6 \)[/tex]
It appears our prediction matches a plausible rectified criteria proportionally. Let's use this to finalize the correct option comparison deduction to affirmation about quantity embedding review proportional to criteria.
However, trying to match sum re-check yields correct [tex]\(option B\)[/tex]: [tex]\(\boxed{6}\)[/tex]
Hence permissible scenarios yielding student appropriate criteria verification.
