Brian saves 2/5 of the $215 he earns each week from his job. If Brian continues to save at this...

1. TRANSLATE the problem information

• Given information:
  • Brian earns \(\$215\) per week
  • He saves \(\frac{2}{5}\) of his weekly earnings
  • We want total savings over 9 weeks

• What this tells us: We need to find his weekly savings first, then multiply by 9 weeks

2. INFER the solution approach

• This is a two-step problem:
  • Step 1: Calculate weekly savings amount
  • Step 2: Multiply weekly savings by 9 weeks
• We cannot skip to the final answer without knowing weekly savings first

3. SIMPLIFY to find weekly savings

• Weekly savings = \(\frac{2}{5} \times \$215\)
• \(\frac{2}{5} \times \$215 = (2 \times \$215) \div 5\)
  \(= \$430 \div 5\)
  \(= \$86\) per week

4. SIMPLIFY to find total savings over 9 weeks

• Total savings = Weekly savings × 9 weeks
• Total savings = \(\$86 \times 9 = \$774\)

Answer: \(\$774\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students try to combine all the numbers at once without recognizing the two-step structure. They might attempt to calculate \(9 \times 215 \times \frac{2}{5}\) in the wrong order, leading to calculation confusion and errors.

This approach often leads to computational mistakes and guessing rather than systematic solution.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify the two steps but make calculation errors, particularly in computing \(\frac{2}{5} \times \$215\). They might calculate this as \(\$430 \div 5\) incorrectly or make errors in the final multiplication \(9 \times \$86\).

These calculation errors lead to selecting an incorrect answer even with the right approach.

The Bottom Line:

This problem tests whether students can break down a rate problem into logical steps rather than trying to work with all given numbers simultaneously. The key insight is recognizing that weekly savings must be calculated before finding total savings over multiple weeks.