Question

At what temperature do the Fahrenheit and Celsius scales give the same reading?

• A. -40${}^o$
• B. 0${}^o$
• C. 574.25${}^o$
• D. 273${}^o$

Answer 1

The correct option is A -40${}^o$

The formulas for converting between degree Celsius and degree Fahrenheit are:

$°F=(°C\ast 9/5)+32$

$°C=(°F-32)\ast 5/9$

To find the temperature when both are equal, we use an old algebra trick and just set ºF = ºC and solve one of the equations.

$°C=(°C\ast 9/5)+32$

$°C-(°C\ast 9/5)=32$

$-4/5\ast °C=32$

$°C=-32\ast 5/4$

$°C=-40$

$°F=(°F\ast 9/5)+32$

$°F-(°F\ast 9/5)=32$

$-4/5\ast °F=32$

$°F=-32\ast 5/4$

$°F=-40$

So the temperature when both the Celsius and Fahrenheit scales are the same is $-40$ degrees.