At what temperature the Fahrenheit and Celsius scales of temperature give the same reading ?.

Options

A. `-40^(@)`
B. `40^(@)`
C. `36.6^(@)`
D. `38^(@)`

Explanation

To find the temperature at which the Fahrenheit and Celsius scales give the same reading, we can set up an equation based on the relationship between the two temperature scales.

### Step-by-Step Solution:

1. **Understand the Conversion Formula**:
The relationship between Celsius (C) and Fahrenheit (F) is given by the formula:
\[ F = \frac{9}{5}C + 32 \]

2. **Set the Two Scales Equal**:
We want to find the temperature where the readings are the same, so we set:
\[ C = F \]
Let’s denote this common temperature as \( X \). Thus, we have:
\[ X = \frac{9}{5}X + 32 \]

3. **Rearrange the Equation**:
To solve for \( X \), we first rearrange the equation:
\[ X - \frac{9}{5}X = 32 \]
This simplifies to:
\[ \frac{5}{5}X - \frac{9}{5}X = 32 \]
\[ -\frac{4}{5}X = 32 \]

4. **Solve for \( X \)**:
Multiply both sides by -5/4 to isolate \( X \):
\[ X = 32 \times -\frac{5}{4} \]
\[ X = -40 \]

5. **Conclusion**:
Therefore, the temperature at which the Fahrenheit and Celsius scales give the same reading is:
\[ \boxed{-40} \]