A student plans a study session consisting of reading segments that last 45 minutes each and practice segments that last...

1. TRANSLATE the problem information

• Given information:
  • Reading segments: 45 minutes each
  • Practice segments: 30 minutes each
  • Total planned study time: 240 minutes
  • Number of reading segments completed: 2
  • Need to find: number of practice segments

2. TRANSLATE into mathematical equation

• Let \(r\) = reading segments and \(p\) = practice segments
• Total time equation: \(45r + 30p = 240\)
• This represents: (time per reading segment × number of segments) + (time per practice segment × number of segments) = total time

3. INFER the solution approach

• Since we know \(r = 2\), we can substitute this value and solve for \(p\)
• Strategy: Substitute known values, then isolate the unknown variable

4. SIMPLIFY through substitution and solving

• Substitute \(r = 2\) into \(45r + 30p = 240\):
  \(45(2) + 30p = 240\)
• Calculate: \(90 + 30p = 240\)
• Isolate the \(p\) term: \(30p = 240 - 90 = 150\)
• Solve for \(p\): \(p = 150 \div 30 = 5\)

Answer: C (5 practice segments)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what the question is asking for or set up the equation incorrectly. They might think they need to find total segments instead of just practice segments, or they might confuse which variable represents what.

For example, they might calculate \(240 \div 45 = 5.33\) and think this relates to the answer, not realizing they need to account for both types of segments.

This leads to confusion and guessing among the answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the equation correctly but make arithmetic errors in the multi-step calculation process.

Common mistakes include:

• \(45 \times 2 = 80\) (instead of 90)
• \(240 - 90 = 160\) (instead of 150)
• \(150 \div 30 = 4\) (miscalculation)

These arithmetic errors may lead them to select Choice B (4) instead of the correct answer.

The Bottom Line:

This problem tests whether students can translate a multi-component time allocation scenario into a linear equation and systematically solve it. Success requires both careful setup and accurate arithmetic execution.