At Which temperature, Both the Fahrenheit and the Centigrade Scales have the same values?
VerifiedExplanation:
The temperature at which both Fahrenheit and Celsius scales show the same numerical value is -40 degrees. This unique point occurs due to the mathematical relationship between these two temperature scales and can be found by setting up a simple equation.
To understand this better, let's recall the conversion formula between Fahrenheit (F) and Celsius (C): F = (9/5)C + 32. At the point where both scales have the same value, we can say F = C. Let's call this common temperature 'x'.
Setting up the equation: x = (9/5)x + 32. Now we can solve for x by rearranging the terms. Subtracting (9/5)x from both sides gives us: x - (9/5)x = 32, which simplifies to: x(1 - 9/5) = 32, or x(-4/5) = 32. Therefore, x = 32 ÷ (-4/5) = 32 × (-5/4) = -40.
This means that -40°F equals -40°C. This temperature is extremely cold and represents conditions that are rarely experienced in most parts of the world, though it can occur in some of the coldest regions during winter months. Understanding this intersection point helps students better grasp the relationship between these two commonly used temperature scales.
