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

1. TRANSLATE the problem information

• Given information:
  • Conversion formula: \(\mathrm{F = \frac{9}{5}C + 32}\)
  • Temperature in Celsius: \(\mathrm{C = 25°}\)
  • Need to find: Temperature in Fahrenheit (F)

2. TRANSLATE the approach

• The phrase "when the temperature is 25 degrees Celsius" tells us to substitute \(\mathrm{C = 25}\) into our formula
• We'll replace C with 25 and calculate F

3. SIMPLIFY through substitution and calculation

• Substitute: \(\mathrm{F = \frac{9}{5}(25) + 32}\)
• Follow order of operations - multiplication before addition:
  • First: \(\mathrm{\frac{9}{5} \times 25 = \frac{9 \times 25}{5} = \frac{225}{5} = 45}\)
  • Then: \(\mathrm{45 + 32 = 77}\)

Answer: \(\mathrm{77°F}\) (Choice C)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly set up the substitution but make arithmetic errors in calculating \(\mathrm{\frac{9}{5} \times 25}\), often getting confused by the fraction multiplication or forgetting to add 32 at the end.

Some students calculate \(\mathrm{\frac{9}{5} \times 25 = 45}\) correctly but then forget the final step of adding 32, leading them to select Choice A (45).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret the conversion process and simply add 32 to the Celsius temperature without applying the \(\mathrm{\frac{9}{5}}\) multiplication factor.

This leads to \(\mathrm{25 + 32 = 57}\), causing them to select Choice B (57).

The Bottom Line:

Temperature conversion problems require careful attention to both the complete formula and precise arithmetic execution. Success depends on systematic substitution followed by accurate multi-step calculations.