A water tank holds 280 liters when full. The tank is drained by 25% of its contents. How many liters...

1. TRANSLATE the problem information

• Given information:
  • Tank capacity: 280 liters
  • Amount drained: \(25\%\) of contents
• What we need to find: How many liters are removed

2. TRANSLATE the calculation needed

• "Drained by 25% of its contents" means we calculate \(25\%\) of 280 liters
• Convert percentage to decimal: \(25\% = 0.25\)
• Set up multiplication: \(0.25 \times 280\)

3. SIMPLIFY to find the answer

• \(0.25 \times 280 = 70\) liters

Answer: C (70)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students confuse what the problem is asking for - they calculate how much water remains instead of how much is removed.

They think: "If 25% is drained, then 75% remains" and calculate \(0.75 \times 280 = 210\) liters.

This may lead them to select Choice D (210).

Second Most Common Error:

Poor percentage conversion: Students make errors in converting \(25\%\) or set up the wrong calculation entirely.

They might calculate \(10\%\) of 280 (thinking \(25\% \approx 20\% \approx 10\%\)) and get 28 liters, or calculate \(20\%\) of 280 and get 56 liters.

This may lead them to select Choice A (28) or Choice B (56).

The Bottom Line:

This problem tests whether students can correctly identify what quantity the problem is asking for (removed vs remaining) and accurately calculate a percentage of a given amount. The key insight is recognizing that "drained by 25%" means 25% is removed, not that 25% remains.