A waiter receives tips from each customer. On average, the tip is 15% of the customer's bill. At this rate,...

1. TRANSLATE the problem information

• Given information:
  • Average tip rate: 15% of customer's bill
  • Customer's bill: $78.20
  • Need to find: Expected tip amount (closest to given choices)

2. TRANSLATE the percentage calculation

• "15% of $78.20" means: \(0.15 \times \$78.20\)
• Convert the percentage: \(15\% = \frac{15}{100} = 0.15\)

3. SIMPLIFY through calculation

• Calculate: \(\$78.20 \times 0.15 = \$11.73\) (use calculator for accuracy)

4. INFER the selection strategy

• The question asks "which is closest to" the calculated tip
• Compare $11.73 to each answer choice:
  1. $8.00 \(\text{(difference: } \$3.73\text{)}\)
  2. $10.00 \(\text{(difference: } \$1.73\text{)}\)
  3. $12.00 \(\text{(difference: } \$0.27\text{)}\)
  4. $14.00 \(\text{(difference: } \$2.27\text{)}\)

5. APPLY CONSTRAINTS to select final answer

• $11.73 is closest in value to $12.00

Answer: C. $12.00

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misunderstand what "15% of" means mathematically and attempt division instead of multiplication. They might calculate \(\$78.20 \div 15 = \$5.21\), then select the closest answer choice.
This may lead them to select Choice A ($8.00) as it's the nearest to their incorrect result.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(0.15 \times \$78.20\) but make calculation errors, such as decimal placement mistakes, leading to results like $117.30 or $1.173.
This leads to confusion and guessing since these values don't align well with any answer choice.

The Bottom Line:

This problem tests whether students can smoothly convert between percentage language and mathematical operations, then recognize when approximation is needed for answer selection.