Q47. - Algebra 2

Question

COFFEE

Some say that to brew an excellent cup of coffee, you must have a brewing temperature of $200{}^{\circ }F$, plus minus five degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

Step-by-Step Solution

Answer

If the brewing temperature for excellent coffee be $x{}^{\circ }F$.

Absolute value equation is $\left|x-200\right|=5$

On solving this equation maximum temperature is $205{}^{\circ }F$ and minimum temperature is $195{}^{\circ }F$

Step 1 - Define variable

Let the brewing temperature for excellent coffee be $x{}^{\circ }F$

Step 2 - Write absolute equation

As the brewing temperature for excellent coffee is $200{}^{\circ }F$ plus minus five degrees

So absolute value equation is obtained by subtracting 200 from x inside the absolute vale symbol and equating it to 5 as shown below

$\left|x-200\right|=5$

Step 3 - Simplify x - 200 = 5

For any real number $a\text{ and }b$ with $b\ge 0$, if $\left|a\right|=b$ then either $a=b$ or $a=-b$ 

So given equation can be written as

$\begin{array}{c}x-200=5\text{ or }x-200=-5\\ x=5+200\text{ or }x=-5+200\\ x=205\text{ or }x=195\end{array}$

So maximum temperature is $205{}^{\circ }F$ and minimum temperature is $195{}^{\circ }F$