Question

What is the temperature at which we get the same reading on both the Centigrade and Fahrenheit scales?

Answer 1

The formulas for converting between degree Celsius

and degree Fahrenheit are:

°F = (°C $\times \frac{9}{5}$) + 32

°C = (°F - 32) $\times \frac{5}{9}$

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$\times \frac{9}{5}$) + 32

°C - (°C$\times \frac{9}{5}$) = 32

$-\frac{4}{5}\times$ °C = 32

$°C=-32\times \frac{5}{4}$

°C = -40

°F = (°F $\times \frac{9}{5}$) + 32

°F - (°F $\times \frac{9}{5}$) = 32

$-\frac{4}{5}\times$ °F = 32

°F = -32 $\times \frac{5}{4}$

°F = -40

So the temperature when both the Celsius and

Fahrenheit scales are the same is -40 degrees.