What temperature has the same value in both the fahrenheit and kelvin scales?

574.25 °

Explanation:

To know this, we need to get the expressions to calculate °F and °K.

In the case of Kelvin:

°K = °C + 273

in fahrenheit:

°F = 9/5 (°C + 32)

Now, in order to know the temperature which both Kelvin and Fahrenheit are the same, we need to use both above equations, and solve for °C.

°C = °K - 273 (1)

°C = 5/9 (°F - 32) (2)

Using 1 and 2 into a same expression:

°K - 273 = 5/9 (°F - 32)

With this, we need to know now the moment which K = F, so, all we need to do is replace the F for the K in the above expression. Doing this, we have:

°K - 273 = 5/9 (°K - 32)

°K = 0.555 (°K - 32) + 273

°K = 5/9K - 17.78 + 273

°K - 5/9K = 255.22

4/9°K = 255.22

°K = 255.22 * 9 / 4

°K = 574.25 °

And this is the temperature in which both Kelvin and Fahrenheit are the same.