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Chapter 16: Problem 17

At what temperature do the Fahrenheit and Celsius scales coincide?

Short Answer

Expert verified
-40 is the temperature at which the Fahrenheit and Celsius scales coincide.

Step by step solution

01

Set up the equation

Set the Fahrenheit (F) temperature equal to the Celsius (C) temperature. Using the conversion formula, replace \(F\) in the equation with \(\frac{9}{5}C + 32\). This results in the equation \(\frac{9}{5}C + 32 = C\).
02

Simplify the equation

Subtract \(C\) from both sides of the equation to isolate \(\frac{9}{5}C\) on one side and \(32-C\) on the other side. This results in \(\frac{9}{5}C - C = 32\).
03

Make \(C\) the subject

First, convert \(C\) to have the same fraction as \(\frac{9}{5}C\), which makes it \(\frac{5}{5}C\). So, the equation becomes \(\frac{9}{5}C - \frac{5}{5}C = 32\), which simplifies to \(\frac{4}{5}C = 32\). Then, multiply both sides of the equation by \(\frac{5}{4}\) to solve for \(C\). The result is \(C = 40\).

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Most popular questions from this chapter

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