At what temperature do the Celsius and Fahrenheit readings have the same numerical value ?

Explanation

To find the temperature at which the Celsius and Fahrenheit readings are the same, we can follow these steps:

### Step 1: Understand the relationship between Celsius and Fahrenheit
The formula that relates Celsius (C) and Fahrenheit (F) is:
\[ F = \frac{9}{5}C + 32 \]

### Step 2: Set the Celsius and Fahrenheit values equal
Since we want to find the temperature where the Celsius and Fahrenheit readings are the same, we can set:
\[ C = F \]
Let’s denote this common temperature as \( X \). Therefore, we can write:
\[ X = \frac{9}{5}X + 32 \]

### Step 3: Rearrange the equation
To solve for \( X \), we first rearrange the equation:
\[ X - \frac{9}{5}X = 32 \]

### Step 4: Combine like terms
We can express \( X \) in terms of a common denominator:
\[ \frac{5}{5}X - \frac{9}{5}X = 32 \]
This simplifies to:
\[ \frac{-4}{5}X = 32 \]

### Step 5: Solve for \( X \)
To isolate \( X \), multiply both sides by \(-\frac{5}{4}\):
\[ X = 32 \times -\frac{5}{4} \]
\[ X = -40 \]

### Conclusion
Thus, the temperature at which the Celsius and Fahrenheit readings are the same is:
\[ \boxed{-40} \]