The table below shows the distribution of US states according to whether they have a state-level sales tax and a...

1. TRANSLATE the problem information

• Given information:
  • Two-way table showing state tax distributions
  • Need: percent of states WITH sales tax that do NOT have income tax

• Key insight: We're looking at a conditional percentage - what percent of one specific group (sales tax states) has a certain characteristic (no income tax).

2. TRANSLATE to identify the correct values

• From the table, states with sales tax:
  • Have income tax: 39 states
  • Don't have income tax: 6 states
  • Total with sales tax: \(39 + 6 = 45\) states

• This means our calculation is: 6 out of 45 states

3. SIMPLIFY to find the percentage

• Calculate the fraction: \(\frac{6}{45}\)
• Convert to decimal (use calculator): \(6 \div 45 = 0.1333...\)
• Convert to percentage: \(0.1333... \times 100\% = 13.333...\%\)
• Round to nearest tenth: \(13.3\%\)

Answer: C. 13.3%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misidentify the denominator by using the total number of states (50) instead of just the states with sales tax (45).

They see "percent of states" and think they need all 50 states as the denominator, calculating \(\frac{6}{50} = 12\%\). This leads them to select Choice B (12.0%).

Second Most Common Error:

Poor TRANSLATE reasoning: Students answer a different question entirely - finding what percent of ALL states have no income tax.

They calculate \(\frac{6 + 1}{50} = \frac{7}{50} = 14\%\), which represents states with no income tax out of all states, not the conditional percentage asked for. This leads them to select Choice D (14.0%).

The Bottom Line:

Two-way table problems require careful attention to conditional relationships. The key is identifying whether you need a percentage of the total population or a percentage within a specific subgroup - in this case, we needed the latter.