The problem asks at what temperature would the difference between Kelvin and Fahrenheit be 50. We are looking for a temperature $T$ such that $K - F = 50$, where $K$ is the temperature in Kelvin and $F$ is the temperature in Fahrenheit.

1. Problem Description

The problem asks at what temperature would the difference between Kelvin and Fahrenheit be

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0. We are looking for a temperature $T$ such that $K - F = 50$, where $K$ is the temperature in Kelvin and $F$ is the temperature in Fahrenheit.

2. Solution Steps

First, we need to express $K$ and $F$ in terms of Celsius, $C$.

The conversion from Celsius to Kelvin is:

$K = C + 273.15$

The conversion from Celsius to Fahrenheit is:

$F = \frac{9}{5}C + 32$

Now, we can substitute these expressions into the equation $K - F = 50$:

$(C + 273.15) - (\frac{9}{5}C + 32) = 50$

$C + 273.15 - \frac{9}{5}C - 32 = 50$

$C - \frac{9}{5}C = 50 + 32 - 273.15$

$-\frac{4}{5}C = 82 - 273.15$

$-\frac{4}{5}C = -191.15$

$C = \frac{5}{4} \cdot 191.15$

$C = 238.9375$

Now we convert $C$ to $K$ and $F$.

$K = C + 273.15 = 238.9375 + 273.15 = 512.0875$

$F = \frac{9}{5}C + 32 = \frac{9}{5}(238.9375) + 32 = 430.0875 + 32 = 462.0875$

We check if $K - F = 50$.

$512.0875 - 462.0875 = 50$

The Celsius temperature is $238.9375$, which gives $K = 512.0875$ and $F = 462.0875$. We are looking for the temperature in Fahrenheit or Kelvin, so we found two possible answers. Usually the convention would be to find the temperature in Fahrenheit. We will round the values to one decimal place.

3. Final Answer

The temperature in Kelvin is approximately $512.1$ K.

The temperature in Fahrenheit is approximately $462.1$ F.

We can express our answer as:

At approximately 462.1 degrees Fahrenheit (or 512.1 Kelvin) the difference between the Kelvin and Fahrenheit temperatures is

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0. Final Answer: 462.1 degrees Fahrenheit.