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Chapter 16: Problem 15

At what temperature do the Fahrenheit and Celsius scales coincide?

Short Answer

Expert verified
The Fahrenheit and Celsius scales coincide at -40 degrees.

Step by step solution

01

Set up the equation

We know that at the given temperature, the values of \emph{Fahrenheit} and \emph{Celsius} are equal. Thus we let the Fahrenheit (F) variable equals Celsius (C) variable in the conversion formula between the two scales. This results in the equation C = 9/5C + 32.
02

Solve for C

The equation from step 1 is then solved for the Celsius (C) variable. First, group all terms with the variable C on one side and the constants on the other side. This results in: -4/5C = 32. Second, divide each side of the equation by -4/5 to solve for C. This computation gives C = -40.
03

Verify the solution

Once the temperature in Celsius is obtained, it is then plugged into the original conversion formula for double checking. This calculation yields: F = 9/5*(-40) + 32 = -40. This confirms that the Fahrenheit and Celsius scales do indeed coincide at -40 degrees.

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