# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Markup

To generate a profit, businesses engage in buying and selling their merchandise. The amount of profit depends on many factors, one of which is the pricing of goods. The selling price covers

1. The costs of buying the goods (e.g., cost of materials to make merchandise, or cost to buy merchandise form supplier);
3. The profit required by the owner to stay in business.

Therefore, we can create the formula:

Selling Price = Cost of Buying + Expenses + Profit

S = C + E + P

The markup, also known as the margin, or gross profit. is the difference between the selling price and operating expenses (M = S - C). The markup also represents the sum of expenses and the profit. Creating the following formulas.

Markup = Expenses + Profit

M = E + P

Selling Price = Cost of Buying + Markup

S = C + M Keep in mind, each formula can be rearranged to solve for the desired variable.

For example, if you are looking for profit, and you are given the expenses, cost, and selling price. Then the formula can be rearranged to

P = S - C - E

## Rate of Markup

Instead of providing the amount of markup, markups may be stated as a percent of (1) cost, or (2) of selling price. Manufacturers usually keep their records in terms of cost, thus, they will use markups as a percent of cost. Whereas, department stores or retailers keep their records in terms of selling price. The following formulas are: $Rate\, of\, Markup\, based\, on\, Cost = \frac{Markup}{Cost} = \frac{M}{C} \times 100\%$

$Rate\, of\, Markup\, based\, on\, Selling\,Price= \frac{Markup}{Selling\,Price} = \frac{M}{S} \times 100\%$

Something to Think About: The rate of markup based on cost can be more than 100%, but the rate of markup based on selling price cannot exceed 100%. What is the reason?

## Examples

Example

A fixture is sold at a price of \$452.20, including markup of 40% of the cost.

a. What is the cost of the fixture?

b. What is the rate of markup on selling price?