Question

At what temperature are the celsius and fahrenheit scale reading equal

Answer 1

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

°F = (°C * 9/5) + 32
°C = (°F - 32) * 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 * 9/5) + 32
°C - (°C * 9/5) = 32
-4/5 * °C = 32
°C = -32 * 5/4
°C = -40

°F = (°F * 9/5) + 32
°F - (°F * 9/5) = 32
-4/5 * °F = 32
°F = -32 * 5/4
°F = -40

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

Answer 2

Let x be the common reading.

Then, C = F = x

Using the formula, C=5/9 (F-32),and substituting x for C and F, we get

x =5/9 (x-32)

x =5/9x - 5/9×32

x - 5/9x = 5×32/9

4/9x = - 5×32/9

x = - 5×32/4 = -40

So, -40C = -40F

Hence, at -40 degrees , the readings on the Celsius scale and the Fahrenheit scales are rhe same.