A bakery surveys 625 customers about two muffin flavors: blueberry and apple. Of those surveyed, 351 prefer blueberry and 274...

1. TRANSLATE the problem information

• Given information:
  • 625 customers surveyed total
  • 351 prefer blueberry muffins
  • 274 prefer apple muffins
  • Bakery will make 5,000 muffins in same proportions
• What we need to find: The difference between blueberry and apple muffin quantities for the 5,000 batch

2. INFER the most efficient approach

• Key insight: Since we only need the difference, we can scale the survey difference directly rather than finding each type separately
• The survey shows \(351 - 274 = 77\) more people prefer blueberry
• This difference proportion will hold for the larger batch

3. SIMPLIFY the scaling calculation

• Survey difference as fraction: \(\frac{77}{625}\) of all customers
• Scale to 5,000 muffins: \(\frac{77}{625} \times 5,000\)
• SIMPLIFY:

\(77 \times 5,000 \div 625\)
\(= 77 \times 8\)
\(= 616\)

Answer: C (616)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skills: Students calculate each muffin type separately (\(\frac{351}{625} \times 5,000 = 2,808\) blueberry and \(\frac{274}{625} \times 5,000 = 2,192\) apple) but then forget to subtract to find the difference.

They see the 2,808 blueberry muffins and select Choice D (2,808), missing the final step entirely.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand what the problem asks for and calculate just the survey difference (\(351 - 274 = 77\)) without scaling it up to the 5,000 muffin batch.

This leads them to select Choice A (77).

The Bottom Line:

This problem tests whether students can work efficiently with proportional relationships and maintain focus on what the question actually asks for. The key is recognizing you can scale differences directly rather than taking the longer path of scaling each part separately.