Q16. - Algebra 2

Question

FOOD 

For exercise 14-16, use the following information.

A meat thermometer is used to assure that a safe temperature has been reached to destroy bacteria. Most meat thermometers are accurate to within plus or minus $2{}^{\circ }F$

16. To what temperature reading should you bake a ham to ensure that the minimum internal temperature is reached? Explain.

Step-by-Step Solution

Answer

Since, thermometer’s accuracy is $\pm 2{}^{\circ }F$. So on baking ham up to $162{}^{\circ }F$, one can check that actual temperature might be $162{}^{\circ }F-2{}^{\circ }F=160{}^{\circ }F$. Thus, ham needs to be baked till thermometer shows $162{}^{\circ }F$ to ensure that minimum temperature is reached.

Step 1 - Meaning of given statement

Let the internal temperature of ham is $x{}^{\circ }F$

Ham needs to reach an internal temperature of $160{}^{\circ }F$

Thermometer’s accuracy is $\pm 2{}^{\circ }F$

Step 2 - Write absolute value equation

As ham needs to reach an internal temperature of $160{}^{\circ }F$ but temperature shown on thermometer is $2{}^{\circ }F$ less than or more than $160{}^{\circ }F$. So in equation form as shown below

$\begin{array}{c}x=160-2\text{ or }x=160+2\\ x-160=-2\text{ or }x-160=2\end{array}$

In absolute value equation it can be written as

$\left|x-160\right|=2$

Step 3 - Simplify x - 160 = 2

To simplify the equation use the definition of absolute value equation as shown below

$\begin{array}{c}x-160=2\\ x=160+2\\ x=162\end{array}$  or  $\begin{array}{c}x-160=-2\\ x=160-2\\ x=158\end{array}$

Thus ham needs to be baked till thermometer shows $162{}^{\circ }F$ to ensure that minimum temperature is reached.