At what temperature do the Fahrenheit and Kelvin scales have the same reading?

Substitute $T_F = X$ into the Fahrenheit to Celsius formula:

$$T_C = \frac{5}{9}(X - 32)$$

Substitute $T_K = X$ into the Kelvin to Celsius formula:

$$T_C = X - 273.15$$

Since both expressions represent the same temperature in Celsius, we can set them equal to each other:

$$\frac{5}{9}(X - 32) = X - 273.15$$

Multiply both sides by 9 to eliminate the fraction:

$$5(X - 32) = 9(X - 273.15)$$

Distribute the numbers on both sides:

$$5X - 160 = 9X - 2458.35$$

Rearrange the terms to isolate $X$:

$$2458.35 - 160 = 9X - 5X$$ $$2298.35 = 4X$$

Divide by 4 to find $X$:

$$X = \frac{2298.35}{4}$$ $$X = 574.5875$$

The temperature at which the Fahrenheit and Kelvin scales have the same reading is 574.5875.

The temperature is $\text{574.5875 degrees Fahrenheit and Kelvin}$.