Question

find the number z for which z degrees F =z degrees C.

Answer 1

The temperature at which both the Celsius and Fahrenheit scales are the same is -40 degrees.

We know the conversion formulas are :
°F = (°C * 9/5) + 32
°C = (°F - 32) * 5/9

Since both are equal at a particular number (temperature is a number), so 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
OR
°F = (°F * 9/5) + 32
°F - (°F * 9/5) = 32
-4/5 * °F = 32
°F = -32 * 5/4
°F = -40