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

Explanation

To find the temperature at which the Fahrenheit and Celsius scales give the same reading, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Fahrenheit and Celsius:**
The formula that relates Celsius (Tc) and Fahrenheit (Tf) is:
\[ Tc = \frac{5}{9}(Tf - 32) \]

2. **Set up the equation for equal readings:**
Since we want to find the temperature at which both scales give the same reading, we set:
\[ Tc = Tf \]
Therefore, we can substitute Tf with Tc in the equation:
\[ Tc = \frac{5}{9}(Tc - 32) \]

3. **Multiply both sides by 9 to eliminate the fraction:**
\[ 9Tc = 5(Tc - 32) \]

4. **Distribute the 5 on the right side:**
\[ 9Tc = 5Tc - 160 \]

5. **Rearrange the equation to isolate Tc:**
Subtract 5Tc from both sides:
\[ 9Tc - 5Tc = -160 \]
This simplifies to:
\[ 4Tc = -160 \]

6. **Solve for Tc:**
Divide both sides by 4:
\[ Tc = \frac{-160}{4} \]
This gives:
\[ Tc = -40 \]

### Conclusion:
The temperature at which the Fahrenheit and Celsius scales give the same reading is **-40 degrees**.