The formula to convert temperature from Celsius to Fahrenheit is F = 9/5C + 32. What is the value of...

1. TRANSLATE the problem information

• Given information:
  • Formula: \(\mathrm{F = \frac{9}{5}C + 32}\)
  • \(\mathrm{F = 212}\)
  • Need to find: C

2. TRANSLATE by substituting the known value

• Substitute \(\mathrm{F = 212}\) into the formula:
  \(\mathrm{212 = \frac{9}{5}C + 32}\)

3. SIMPLIFY by isolating the C term

• Subtract 32 from both sides:
  \(\mathrm{212 - 32 = \frac{9}{5}C}\)
  \(\mathrm{180 = \frac{9}{5}C}\)

4. SIMPLIFY by solving for C

• Multiply both sides by 5/9 (the reciprocal of 9/5):
  \(\mathrm{180 \times \frac{5}{9} = C}\)
• Calculate: \(\mathrm{180 \times \frac{5}{9} = \frac{900}{9} = 100}\)
• Therefore: \(\mathrm{C = 100}\)

Answer: C) 100

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when multiplying \(\mathrm{180 \times \frac{5}{9}}\), either by incorrectly calculating the fraction multiplication or by mixing up whether to multiply by 5/9 or 9/5.

For example, if they multiply by 9/5 instead: \(\mathrm{180 \times \frac{9}{5} = 324}\), which doesn't match any answer choice. This leads to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY sequencing: Students might try to multiply by 5/9 before subtracting 32, leading to more complex calculations and potential errors.

This disrupted order of operations can lead them to calculate incorrectly and select Choice D (180) by stopping at the intermediate step where \(\mathrm{180 = \frac{9}{5}C}\).

The Bottom Line:

This problem tests systematic algebraic manipulation. Success requires careful attention to inverse operations and fraction arithmetic - skills that seem simple but are easy to execute incorrectly under test pressure.