Question

At what temperature do the Celsius and Fahrenheit temperature scales have the same numeric value? a) -40 degrees b) 0 degrees c) 40 degrees d) 100 degrees

Short answer

a) -40 degrees b) 0 degrees c) 40 degrees d) 100 degrees Answer: a) -40 degrees

Step-by-step solution

Set up the equation

Since we're looking for when the Celsius and Fahrenheit scales have the same numeric value, we can represent that as: C = F Now, let's use the Fahrenheit to Celsius conversion formula and replace F with C: C = (9/5) * C + 32

Solve for C

To solve for C, we need to get C by itself on one side of the equation: C - (9/5) * C = 32 First, let's get a common denominator to combine the C terms. This means multiplying the first term (C) by 5/5: (5/5) * C - (9/5) * C = 32 This simplifies to: (5 - 9) / 5 * C = 32 Now we have: -4/5 * C = 32 To get C by itself, we will multiply both sides of the equation by -5/4: C = 32 * (-5/4) This simplifies to: C = -40 So the Celsius temperature at which the Celsius and Fahrenheit temperature scales have the same numeric value is -40 degrees, which corresponds to option (a).