What is the temperature at which Fahrenheit and Celsius are equal?

[Dan Monaghan]

I'm doing some problems for physics at the end of one the chapters and I get to a question that asks
"At what temperature does Fahrenheit and Celsius have the same numerical value?"

Now the answer is -40, but I'm not sure how this answer was established. Between class, lab and study time, I've been pouring over physics for the last 7 hours and I'm toasted. I have a feeling that the answer is pretty simple, but I can't seem to get it. Does anybody have any answers?

 

[Defennder]

Well you just have to equate the temperature in one scale to the formula for conversion in the other scale and solve the unknown, right?

 

[symbolipoint]

from Dan Monaghan:

I get to a question that asks
"At what temperature does Fahrenheit and Celsius have the same numerical value?"

That is simple first-year high school Algebra. You barely need any physics knowledge at all. F: fahrenheit, water boils at ~212, freezes at ~32. C: Celsius, water boils at 100, freezes at 0. Find the linear equation.

 

[Alex6200]

F = (9/5)C + 32
We're looking for an F where F = C, so

F = (9/5)F + 32

-(4/5)F = 32

F = -32 * 5/4

F = -40

So at -40 degrees the Celsius value is the same as the Fahrenheit value.