The price of an item increased from $75 to $90. What is the percent increase in the price? 15 18...

1. TRANSLATE the problem information

• Given information:
  • Original price: \(\$75\)
  • New price: \(\$90\)
  • Need to find: percent increase

• What this tells us: We need to calculate how much the price increased as a percentage of the original price.

2. SIMPLIFY using the percent increase formula

• Apply the formula: \(\mathrm{Percent\ increase} = \frac{\mathrm{new\ value} - \mathrm{original\ value}}{\mathrm{original\ value}} \times 100\)
• Calculate the increase: \(\$90 - \$75 = \$15\)
• Calculate the percent:
  \(\frac{15}{75} \times 100\)
  \(= 0.2 \times 100\)
  \(= 20\%\)

Answer: C) 20

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when calculating \(15 \div 75\), getting \(0.25\) instead of \(0.2\).

When \(15 \div 75 = 0.25\), then \(0.25 \times 100 = 25\%\), leading them to think the answer is \(25\%\).

This may lead them to select Choice D (25).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse the actual increase amount (\(\$15\)) with the percent increase and think the answer should be \(15\%\).

They see that the price went up by \(\$15\) and mistakenly believe this directly represents \(15\%\) increase without considering it as a fraction of the original price.

This may lead them to select Choice A (15).

The Bottom Line:

This problem requires careful attention to the percent increase formula and precise arithmetic. Students must resist the temptation to use the dollar increase amount as the percentage and must execute the division \(15 \div 75\) accurately.