The problem asks at what temperature is the difference between Fahrenheit and Celsius equal to 50 degrees.

1. Problem Description

The problem asks at what temperature is the difference between Fahrenheit and Celsius equal to 50 degrees.

2. Solution Steps

Let $F$ be the temperature in Fahrenheit and $C$ be the temperature in Celsius.

We are given that $F - C = 50$.

We know the formula to convert Celsius to Fahrenheit is:

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

Now, we can substitute this formula into our equation:

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

Combine the terms with $C$:

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

$\frac{9}{5}C - \frac{5}{5}C = 18$

$\frac{4}{5}C = 18$

Multiply both sides by $\frac{5}{4}$:

$C = 18 \cdot \frac{5}{4}$

$C = \frac{90}{4}$

$C = \frac{45}{2}$

$C = 22.5$

Now, we can find the Fahrenheit temperature:

$F = \frac{9}{5}(22.5) + 32$

$F = \frac{9}{5} \cdot \frac{45}{2} + 32$

$F = \frac{9 \cdot 9}{2} + 32$

$F = \frac{81}{2} + 32$

$F = 40.5 + 32$

$F = 72.5$

We can check if the difference is 50:

$F - C = 72.5 - 22.5 = 50$

3. Final Answer

The temperature is 22.5 degrees Celsius or 72.5 degrees Fahrenheit.