Which expression represents the result of increasing a positive quantity w by 43%?

1. TRANSLATE the problem information

• Given information:
  • We need to increase quantity w by 43%
  • We want the expression that represents this result

2. INFER what "increase by 43%" means mathematically

• Increasing by 43% means we add 43% of the original to the original amount
• This gives us: \(\mathrm{original + (43\% \ of\ original)}\) = \(\mathrm{w + 0.43w}\) = \(\mathrm{1.43w}\)
• Alternatively: increasing by 43% means the result is 143% of the original = \(\mathrm{1.43w}\)

3. Check our logic against the answer choices

• A. \(\mathrm{1.43w}\) matches our calculation ✓
• B. \(\mathrm{0.57w}\) represents 57% of original (a decrease of 43%)
• C. \(\mathrm{43w}\) represents 4300% of original (increase of 4200%)
• D. \(\mathrm{0.43w}\) represents just 43% of original (not an increase by 43%)

Answer: A. \(\mathrm{1.43w}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse "increase by 43%" with "43% of the original quantity"

They think: "43% means 0.43, so the answer must be \(\mathrm{0.43w}\)"

This reasoning misses that we want the result after increasing, not just the amount of the increase. This may lead them to select Choice D (\(\mathrm{0.43w}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse increase with decrease

They might think: "If we increase by 43%, we have \(\mathrm{100\% - 43\% = 57\%}\) remaining" (applying decrease logic incorrectly)

This may lead them to select Choice B (\(\mathrm{0.57w}\)).

The Bottom Line:

The key insight is distinguishing between "the amount of increase" (which is \(\mathrm{0.43w}\)) and "the result after increasing" (which is \(\mathrm{w + 0.43w = 1.43w}\)). Students often select the amount of increase rather than the final result.