Chapter 8.5, Problem 31HP

To determine

An equation and find the value of temperature in degrees Fahrenheit

Answer to Problem 31HP

The solution of the equation is $C=-40$

Explanation of Solution

Given:

The formula $F=1.8C+32$ can be used to find the temperature in degrees Fahrenheit F and $F=C$

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the equation when $F=C$ as below:

  $C=1.8C+32$

In order to solve the equation $C=1.8C+32$ first subtract both sides by $1.8C$ and then divide both sides by $-0.8$ and then simplify further as below:

  $\begin{array}{c}C=1.8C+32\\ C-1.8C=1.8C+32-1.8C\\ -0.8C=32\\ \frac{-0.8C}{-0.8}=\frac{32}{-0.8}\\ C=-40\end{array}$

Thus, the solution of the equation is $C=-40$