Question

A machine is used to fill each of several bags with 16 ounces of sugar. After the bags are filled, another machine weighs them. If the bag weighs $0.3$ounce more or less than the desired weight, the bag is rejected. Write an equation to find the heaviest and lightest bag the machine will approve.

Short answer

Heaviest bag approve is of 16.3 ounces or lightest bag approve is of 15.7 ounces

Step-by-step solution

- Define variable

Let the actual weight of sugar bag be x ounces

- Write absolute equation

As the sugar bag approved has weight 16 ounces plus minus 0.3 ounce.

So absolute value equation is obtained by subtracting 16 from x inside the absolute vale symbol and equating it to 0.3 as shown below

$\left|x-16\right|=0.3$

- Simplify x-16=0.3

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

$\begin{array}{c}x-16=0.3\text{or}x-16=-0.3\\ x=0.3+16\text{or}x=-0.3+16\\ x=16.3\text{or}x=15.7\end{array}$

So heaviest bag approve is of 16.3 ounces or lightest bag approve is of 15.7 ounces.