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

Options

A. `-40^@`
B. `0^@`
C. `574.25^@`
D. `273^@`

Explanation

To find the temperature at which the Fahrenheit and Celsius scales give the same reading, we can use the relationship between the two temperature scales. The formula to convert Celsius (C) to Fahrenheit (F) is:

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

We want to find the temperature (let's call it \( x \)) where \( F = C \). Therefore, we can set up the equation:

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

### Step 1: Set up the equation
We start with the equation where Fahrenheit equals Celsius:
\[ x = \frac{9}{5}x + 32 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply every term by 5:
\[ 5x = 9x + 160 \]

### Step 3: Rearrange the equation
Next, we rearrange the equation to isolate \( x \):
\[ 5x - 9x = 160 \]
\[ -4x = 160 \]

### Step 4: Solve for \( x \)
Now, we divide both sides by -4 to solve for \( x \):
\[ x = \frac{160}{-4} \]
\[ x = -40 \]

### Conclusion
The temperature at which the Fahrenheit and Celsius scales give the same reading is:
\[ x = -40 \, \text{degrees} \]