The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total cost,...

1. TRANSLATE the problem information

• Given information:
  • Original shirt cost: \(\$20\)
  • Sales tax rate: \(5\%\)
  • Need to find: Total cost including tax

2. INFER the approach needed

• Total cost = Original cost + Tax amount
• First we need to calculate the tax amount, then add it to the original cost

3. TRANSLATE percentage to decimal and SIMPLIFY the tax calculation

• Convert 5% to decimal: \(5\% = 0.05\)
• Calculate tax amount: \(0.05 \times \$20 = \$1.00\)

4. SIMPLIFY to find total cost

• Total cost = \(\$20 + \$1 = \$21\)

Answer: C. \(\$21.00\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret what "5% sales tax" means mathematically. Instead of calculating 5% of the \(\$20\) cost, they might think the tax is simply \(\$0.05\).

This leads to: \(\$20 + \$0.05 = \$20.05\)

This may lead them to select Choice A (\(\$20.05\))

Second Most Common Error:

Poor percentage conversion: Students might convert 5% incorrectly, perhaps thinking \(5\% = 0.5\) instead of \(0.05\).

This leads to: \(0.5 \times \$20 = \$10\), then \(\$20 + \$10 = \$30\), or they might make other calculation errors that result in \(\$20.50\).

This may lead them to select Choice B (\(\$20.50\))

The Bottom Line:

This problem tests whether students can correctly translate percentage language into mathematical operations and understand the basic concept that sales tax is calculated as a percentage of the original cost, then added to find the total.