Question

At what temperature, the temperature on Celsius and Fahrenheit scales equal?

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

Answer 1

The correct option is C $-{40}^o$ Celsius

We have the formulas for converting between degree Celsius to degree Fahrenheit are;

${}^{0}F={(}^{0}C\times \frac{9}{5})+32$

${}^{0}C={(}^{0}F-32)\times \frac{5}{9}$

It does not matter which equation you use; simply use $x$ instead of degrees Celsius and Fahrenheit. You can solve this problem by solving for $x$;

${}^{0}C=\frac{5}{9}\times {(}^{0}F-32)$

$x=\frac{5}{9}\times (x-32)$

$x=\left(\frac{5}{9}\right)x-17.778$

$0.444x=-17.778$

$x=-40degreeCelsiusorFahrenheit$.

Working using the other equation, we get the same answer;

${}^{0}F={(}^{0}C\times \frac{9}{5})+32$

${}^{0}x-{(}^{0}x\times \frac{9}{5})=32$

$-\frac{4}{5}{\times }^{0}x=32$

${}^{0}x=-32\times \frac{5}{4}$

$x=-40degreeCelsiusorFahrenheit$

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