Q5. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

The amount of soda, in fluid ounces, dispensed from a machine must satisfy the equation $|a-0.4|=20.$ Which of the following graphs shows the acceptable minimum and maximum amounts that can be dispensed from the machine?

Step-by-Step Solution

Answer

The $20.4$ and $-19.6$ maximum and minimum amounts that can be dispensed from the machine respectively.

Step 1. Given information.

An equation for the amount of soda in fluid ounces dispensed from a machine:

$|a-0.4|=20$

To find the maximum and minimum number which is satisfy the given equation.

Step 2. To find the value of a.

$|a-0.4|=20$

It is a modulus function.

So, here will exist two cases

$\begin{array}{l}Case1:\\ a-0.4=20\\ \Rightarrow a=20+0.4\\ \Rightarrow a=20.4\\ Case2:\\ a-0.4=-20\\ \Rightarrow a=-20+0.4\\ \Rightarrow a=-19.6\end{array}$

Step 3. Conclusion.

Therefore, the $20.4$ and $-19.6$ maximum and minimum amounts that can be dispensed from the machine respectively.

Hence, the correct option is A.