There were approximately 113,000 occupational therapy jobs in the United States in 2012. The Bureau of Labor Statistics has projected...

1. TRANSLATE the problem information

• Given information:
  • 2012 jobs: \(113,000\)
  • Projected increase: \(29\%\) from 2012 to 2022
  • Need to find: Total jobs in 2022

• What this tells us: We need to calculate what \(113,000\) becomes after a \(29\%\) increase

2. TRANSLATE the percentage increase concept

• "Increase by \(29\%\)" means the new amount = original amount + \(29\%\) of original amount
• This can be calculated as:
  \(\mathrm{New\ amount = Original \times (1 + 0.29)}\)
  \(\mathrm{New\ amount = Original \times 1.29}\)
• So we need: \(113,000 \times 1.29\)

3. SIMPLIFY the calculation

• \(113,000 \times 1.29 = 145,770\) (use calculator)
• Looking at answer choices, \(145,770\) is closest to \(145,800\)

Answer: D. 145,800

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misunderstanding what "increase by \(29\%\)" means

Students often think "increase by \(29\%\)" means "add 29" or "add 2,900" instead of adding \(29\%\) of the original amount. They might calculate:

• \(113,000 + 29 = 113,029\) (way too small)
• \(113,000 + 2,900 = 115,900\)

This may lead them to select Choice A (115,900)

Second Most Common Error:

Poor TRANSLATE reasoning: Confusing \(29\%\) with \(2.9\%\)

Students might convert \(29\%\) incorrectly as \(2.9\%\) and calculate:
\(113,000 \times 1.029 = 116,277\)

This may lead them to select Choice B (116,300)

The Bottom Line:

The key challenge is correctly interpreting "increase by \(29\%\)" as multiplying by \(1.29\), not just adding some version of 29 to the original number.