Chapter 6.2, Problem 36PFA

To determine

To find: An equation to form system of equations .

Answer to Problem 36PFA

  $2C=F$

Option B.

Explanation of Solution

Given information:

  $F=\frac{9}{5}C+32$

C represents temperature in degrees Celsius.

F represents temperature in degrees Fahrenheit.

Temperature in Fahrenheit is double the Temperature in Celsius scale.

  $F=\frac{9}{5}C+32$ --------(1)

Temperature in Fahrenheit is double the Temperature in Celsius scale means $F=2C$

  $F=2C$ -------(2)

Substituting value of F from equation (2) in equation (1)

We get

  $\begin{array}{l}F=\frac{9}{5}C+32\\ \Rightarrow 2C=\frac{9}{5}C+32\\ \Rightarrow 2C-\frac{9}{5}C=32\\ \Rightarrow \frac{10C-9C}{5}=32\\ \Rightarrow \frac{1}{5}C=32\\ \Rightarrow C=160\end{array}$

Substitute value of C in equation-(2)

We get

  $\begin{array}{l}F=2C\\ \Rightarrow F=2\left(160\right)\\ \Rightarrow F=320\end{array}$

Here we got values of temperature in

Celsius scale = $C=160$ degrees

Fahrenheit scale = $F=320$ degrees.

So we got temperature in Fahrenheit scale is double that of temperature in Celsius scale using $2C=F$

So $2C=F$ is the correct Answer.