A table of the US minimum wage for 6 different years is shown below.YearUS minimum wage (dollars per hour)19601.0019701.6019803.1019903.8020005.152010...

1. TRANSLATE the problem information

• Given information:
  • 1960 minimum wage: \(\$1.00\) per hour
  • 1970 minimum wage: \(\$1.60\) per hour
  • Need: percent increase from 1960 to 1970

• What this tells us: We need to find how much the wage increased as a percentage of the original 1960 wage.

2. INFER the correct approach

• Since we want percent increase, we need the percent increase formula
• The "from" year (1960) becomes our base/old value
• The "to" year (1970) becomes our new value
• Formula: \(\mathrm{Percent\,increase} = \frac{\mathrm{New\,Value} - \mathrm{Old\,Value}}{\mathrm{Old\,Value}} \times 100\%\)

3. SIMPLIFY the calculation

• Substitute into formula:
  \(\mathrm{Percent\,increase} = \frac{1.60 - 1.00}{1.00} \times 100\%\)

• Calculate the difference: \(1.60 - 1.00 = 0.60\)

• Divide by old value: \(\frac{0.60}{1.00} = 0.60\)

• Convert to percentage: \(0.60 \times 100\% = 60\%\)

Answer: B. 60%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Using 1970 as the base value instead of 1960

Students sometimes get confused about which year should be in the denominator. They might calculate:

\(\frac{1.60 - 1.00}{1.60} \times 100\% = \frac{0.60}{1.60} \times 100\% = 37.5\%\)

While this isn't exactly any of the given choices, it shows the conceptual confusion about the base value.

Alternatively, they might calculate:

\(\frac{1.00}{1.60} \times 100\% = 62.5\%\)

thinking this represents the "percent increase."

This may lead them to select Choice C (62.5%).

Second Most Common Error:

Poor TRANSLATE reasoning: Misinterpreting what "percent increase" means

Some students might think they need to find what percentage 1970 wage is of 1960 wage, calculating:

\(\frac{1.60}{1.00} \times 100\% = 160\%\)

They then mistakenly think this 160% IS the percent increase, rather than recognizing that a 60% increase results in 160% of the original.

This leads to confusion and guessing since 160% isn't among the choices.

The Bottom Line:

Percent increase problems require careful attention to which value serves as the base. The key insight is that "increase FROM year A TO year B" means year A provides the denominator in your calculation.