Mathematics » Introducing Percents » Solve Sales Tax, Commission, and Discount Applications

# Solving Mark-up Applications

## Solving Mark-up Applications

Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price. The retailer then adds a mark-up to the wholesale price to get the list price, the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate. To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.

### Definition: Mark-up

The mark-up is the amount added to the wholesale price.

$$\begin{array}{ccc}\hfill \text{amount of mark-up}& =& \text{mark-up rate}·\text{wholesale price}\hfill \\ \hfill \text{list price}& =& \text{wholesale price}+\text{mark up}\hfill \end{array}$$

The list price should always be more than the wholesale price.

## Example

Adam’s art gallery bought a photograph at the wholesale price of $$\text{\250}.$$ Adam marked the price up $$\text{40%}.$$ Find the amount of mark-up and the list price of the photograph.

### Solution

 Identify what you are asked to find. What is the amount of mark-up? Choose a variable to represent it. Let $$m=$$ the amount of each mark-up. Write a sentence that gives the information to find it. The mark-up is 40% of the wholesale price. Translate into an equation. Simplify. Check if this answer is reasonable. Yes. The markup rate is less than 50% and \$100 is less than half of \$250. Write a complete sentence that answers the question. The mark-up on the photograph was \$100.  Identify what you are asked to find. What is the list price? Choose a variable to represent it. Let $$p=$$ the list price. Write a sentence that gives the information to find it. The list price is the wholesale price plus the mark-up. Translate into an equation. Simplify. Check if this answer is reasonable. Yes. The list price, \$350, is more than the wholesale price, \$250. Write a complete sentence that answers the question. The list price of the photograph was \$350.