The formula to convert temperature from degrees Celsius to degrees Fahrenheit is F = 9/5 C + 32. For what...

1. TRANSLATE the problem information

• Given information:
  • Conversion formula: \(\mathrm{F = \frac{9}{5}C + 32}\)
  • Temperature in Fahrenheit: \(\mathrm{F = 68}\)
  • Need to find: the value of C

2. TRANSLATE the question into an equation

• The question asks "For what value of C is F = 68?"
• This means we substitute \(\mathrm{F = 68}\) into our formula:
  \(\mathrm{68 = \frac{9}{5}C + 32}\)

3. SIMPLIFY by isolating the term with C

• Subtract 32 from both sides:
  \(\mathrm{68 - 32 = \frac{9}{5}C}\)
  \(\mathrm{36 = \frac{9}{5}C}\)

4. SIMPLIFY to solve for C

• To get C by itself, multiply both sides by (5/9):
  \(\mathrm{36 \times \frac{5}{9} = C}\)
• Calculate: \(\mathrm{C = \frac{36 \times 5}{9} = \frac{180}{9} = 20}\)

Answer: \(\mathrm{20°C}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when calculating \(\mathrm{36 \times \frac{5}{9}}\)

Many students correctly set up the equation and get to \(\mathrm{36 = \frac{9}{5}C}\), but then struggle with the fraction multiplication. They might calculate \(\mathrm{36 \times \frac{5}{9}}\) incorrectly, getting values like 16 or 200 instead of 20. This leads to confusion and potentially guessing among answer choices.

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which temperature goes where in the equation

Some students might incorrectly set up the equation as \(\mathrm{C = \frac{9}{5} \times 68 + 32}\), treating 68 as if it were the Celsius temperature instead of the Fahrenheit temperature. This fundamental misunderstanding of what the problem is asking leads them far from the correct answer.

The Bottom Line:

This problem tests both equation setup skills and fraction arithmetic. Success requires carefully reading what temperature scale is given (Fahrenheit = 68) and accurately performing the reciprocal multiplication to isolate the variable.