# Solving Simple Equations

In accounting, the equations you will use are not overly complicated, but you will need to know how to calculate simple equations. For example, calculating wages uses an equation like this:

\newcommand{\ctext}{\style{font-family:Arial}{\text{#1}}} \begin{align*} \ctext{Wages} &= \ctext{Number of hours worked} \times \ctext{Pay rate} \cr &= 35 \ctext{ hours} \times 17.50 \cr &= 612.50 \end{align*}

In this example, we want to calculate the number of shirts we need to produce to make a profit of $100,000. The equation we use to calculate this is; $$\ctext{Number of units (shirts) required} = \cfrac{\left(\ctext{Fixed costs} + \ctext{target profit}\right)}{\ctext{Contribution margin per unit}}$$ We will use the following information; Target profit = \$100,000
Fixed costs = \$50,000 Contribution margin per unit = \$10

## Step 1 – Use the equation

$$\ctext{Number of units (shirts) required} = \frac{\left(\ctext{Fixed costs} + \ctext{target profit}\right)}{\ctext{Contribution margin per unit}}$$

## Step 2 – Substitute figures into the equation

$$\ctext{Number of units (shirts) required} = \frac{(50,000 + 100,000)}{10}$$

## Step 3 – Solve the equation

\begin{align*} \ctext{Number of units (shirts) required} &= \frac{150,000}{10} \cr &= 15,000 \ctext{ units} \end{align*}

Therefore, we would need to produce and sell 15,000 shirts to make our target profit of \\$100,000.