Fahrenheit and Celsius are the two scales used for measuring temperature. If the numerical value of a temperature recorded in both the scales is found to be same, what is the temperature?

The Fahrenheit and Celsius scales are related by the linear conversion formula F = (9/5)C + 32. To find the temperature where both scales yield the same numerical value, we set F = C in the equation. This results in the algebraic expression C = (9/5)C + 32. Subtracting (9/5)C from both sides gives -4/5C = 32, which simplifies to C = -160/4, or -40. Therefore, -40°C is exactly equal to -40°F. This is the unique intersection point for these two scales because they have different reference points for the freezing and boiling of water but a linear relationship that converges at this specific negative value. Other temperatures, such as +40°, do not share this property as the scales diverge further apart as temperatures increase.