Chapter 1.4, Problem 22PPS

To determine

To write: and solve an equation describing the maximum and minimum temperature.

Answer to Problem 22PPS

The maximum temperature is $325°$.

The minimum temperature is $275°$.

Explanation of Solution

Given information:

The ideal temperature for roasting cocoa beans is $300°$ plus or minus $25°$.

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

More over

  $\begin{array}{l}\left|x+a\right|=b\\ \Rightarrow x+a=b\text{or}x+a=-b\end{array}$

Calculation:

Consider the given condition,

The ideal temperature for roasting cocoa beans is $300°$ plus or minus $25°$.

So, the corresponding absolute value equation can be written as

  $\left|x-300°\right|=25°$

Now, solve the equation as shown,

  $\begin{array}{c}\left|x-300°\right|=25°\\ x-300°=25°\text{or}x-300°=-25°\\ x-300°+300°=25°+300°\text{or}x-300°+300°=-25°+300°\\ x=325°\text{or}x=275°\end{array}$

Hence, the maximum temperature is $325°$ and he minimum temperature is $275°$.