Question

At which temperature, magnitude of \( ^\circ C \) and \( ^\circ F \) are equal?

• A. 273
• B. 40
• C. -40
• D. -273

Hint:

Only one temperature where \( ^\circ C = ^\circ F \): \(-40^\circ\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Temperature scales are linear functions of each other. We need to find the specific value where the numerical reading on the Celsius scale matches the numerical reading on the Fahrenheit scale.
Step 2: Key Formula or Approach:
The relationship between Celsius (\( C \)) and Fahrenheit (\( F \)) is:
\[ \frac{C}{5} = \frac{F - 32}{9} \]
Step 3: Detailed Explanation:
We are looking for the point where \( C = F \). Let this value be \( x \).
\[ \frac{x}{5} = \frac{x - 32}{9} \]
Cross-multiplying to solve for \( x \):
\[ 9x = 5(x - 32) \]
\[ 9x = 5x - 160 \]
\[ 4x = -160 \]
\[ x = -40 \]
Therefore, at \(-40^\circ\), the Celsius and Fahrenheit scales indicate the same value.
Step 4: Final Answer:
The temperature is \(-40\).