At what temperature do the Celsius and Fahrenheit readings have the same numerical value ? a) 273 b) −273 c) −40 d) 40

Options

A. 273
B. `-273`
C. `-40`
D. 40

Explanation

To find the temperature at which the Celsius and Fahrenheit readings are the same, we can use the conversion formula between the two temperature scales:

\[ F = \frac{9}{5}C + 32 \]

Where:
- \( F \) is the temperature in Fahrenheit.
- \( C \) is the temperature in Celsius.

We want to find the temperature where \( F = C \). Therefore, we can set \( F \) equal to \( C \) in the equation:

\[ C = \frac{9}{5}C + 32 \]

Now, let's solve for \( C \):

1. **Rearranging the equation**:
\[ C - \frac{9}{5}C = 32 \]

2. **Combining like terms**:
\[ \frac{5}{5}C - \frac{9}{5}C = 32 \]
\[ -\frac{4}{5}C = 32 \]

3. **Multiplying both sides by -5/4 to solve for C**:
\[ C = 32 \times -\frac{5}{4} \]
\[ C = -40 \]

Thus, the temperature at which the Celsius and Fahrenheit readings are the same is:

**Final Answer: \( C = -40 \)**

This corresponds to option (c) -40.