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

Explanation

To solve the problem of finding the temperature at which the Fahrenheit and Celsius scales give the same reading, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We know the relationship between the Fahrenheit (Tf) and Celsius (Tc) scales is given by the formula:
\[ Tf = 1.8 \times Tc + 32 \]

2. **Setting the Equivalence**:
Since we want to find the temperature at which both scales read the same, we can set:
\[ Tf = Tc = T \]
Therefore, we can rewrite the equation as:
\[ T = 1.8 \times T + 32 \]

3. **Rearranging the Equation**:
To isolate T, we can rearrange the equation:
\[ T - 1.8 \times T = 32 \]
This simplifies to:
\[ -0.8 \times T = 32 \]

4. **Solving for T**:
Now, we can solve for T by dividing both sides by -0.8:
\[ T = \frac{32}{-0.8} \]
Simplifying this gives:
\[ T = -40 \]

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

### Final Answer:
At -40 degrees, both the Fahrenheit and Celsius scales read the same.

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