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

Explanation

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

### Step 1: Understand the relationship between the temperature scales
The formula to convert Celsius (C) to Fahrenheit (F) is:
\[ F = 1.8C + 32 \]
And the relationship between Celsius (C) and Kelvin (K) is:
\[ C = K - 273.15 \]

### Step 2: Substitute the Kelvin equation into the Fahrenheit equation
Since we want to find the temperature where Fahrenheit (Tf) equals Kelvin (T), we can substitute \( C \) in the Fahrenheit equation with \( K - 273.15 \):
\[ Tf = 1.8(K - 273.15) + 32 \]

### Step 3: Set Tf equal to K
Since we are looking for the temperature where the two scales give the same reading, we can set \( Tf \) equal to \( K \):
\[ K = 1.8(K - 273.15) + 32 \]

### Step 4: Simplify the equation
Distributing the 1.8:
\[ K = 1.8K - 1.8 \times 273.15 + 32 \]
This simplifies to:
\[ K = 1.8K - 491.67 + 32 \]
\[ K = 1.8K - 459.67 \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( K \):
\[ K - 1.8K = -459.67 \]
\[ -0.8K = -459.67 \]

### Step 6: Solve for K
Dividing both sides by -0.8 gives:
\[ K = \frac{459.67}{0.8} \]
Calculating this gives:
\[ K = 574.59 \]

### Conclusion
Thus, the temperature at which the Fahrenheit and Kelvin scales give the same reading is:
\[ K = 574.59 \]