At what temperature does the numerical value in degrees Fahrenheit (°F) equal the numerical value in degrees Celsius (°C)?

• A. 100
• B. 0
• C. 32
• D. -40

Answer: (D)

Verified step by step guidance

1. Recall the formula that relates temperature in degrees Celsius (\( C \)) to degrees Fahrenheit (\( F \)): \[ F = \frac{9}{5} C + 32 \]
2. Set the temperature values equal to each other because the problem asks for the temperature where \( F = C \). So, replace \( F \) with \( C \) in the equation: \[ C = \frac{9}{5} C + 32 \]
3. Rearrange the equation to isolate \( C \) on one side: \[ C - \frac{9}{5} C = 32 \]
4. Combine like terms by factoring out \( C \): \[ C \left(1 - \frac{9}{5}\right) = 32 \]
5. Solve for \( C \) by dividing both sides by the factor in parentheses: \[ C = \frac{32}{1 - \frac{9}{5}} \] This will give the temperature where the Celsius and Fahrenheit scales have the same numerical value.