Question

For a company to invest in a product, they must believe they will receive a 12% return on the investment (ROI) plus or minus 3%. Write an equation to find the least and the greatest ROI they believe they will receive

Short answer

The equation that represents the least and greatest ROI is $\left|x-12\right|=3$.

Least ROI will be 9%.

Greatest ROI will be 15%.

Step-by-step solution

Step-1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means the positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$will always be positive and hence the absolute value.

Step-3. Solution of the given problem.

The company believes they will receive 12% ROI plus or minus 3%.

Let the ROI that the company receives be x.

Then, according to the given statement, the equation will be:

$x=12\%\pm 3\%$.

This implies, $\left|x-12\right|=3$.

On solving the equation two cases occurs: -

Case 1: -$x-12=3$

Add 12 to both sides of the equation.

$\begin{array}{l}x-12+12=3+12\\ x=15\end{array}$

Case 2: -$x-12=-3$

Add 12 to both sides of the equation.

$\begin{array}{l}x-12+12=-3+12\\ x=9\end{array}$

Therefore,

The least ROI that the company will receive is 9%.

The greatest ROI that the company will receive is 15%.

The equation for that is $\left|x-12\right|=3$.