### Learning OUTCOME

- Use mathematical notation to solve markup problems

Ana runs Blue Boat Designs, where she makes colorful beaded earrings. She sells her earrings to boutiques around Los Angeles for [latex]$18[/latex]. A shop called Treasure Hunt purchases Ana’s earrings for [latex]$18[/latex], marks them up [latex]50\%[/latex] and then sells them to shop customers for [latex]$27[/latex].

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.

### Mark-up

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

**amount of mark-up = mark-up rate [latex]\cdot[/latex] wholesale price**

**list price = wholesale price + mark up**

The list price should always be more than the wholesale price, or it would be a mark-down, not a mark-up.

The mark-up rate can be less than, equal to, or greater than [latex]100\%[/latex].

### example

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

### try it

### TRY IT

### EXAMPLE

A very common mark-up strategy in retail stores is to simply double the price they paid for the item. Let’s walk through how you would calculate the mark-up rate for this situation.

Braided Salon purchases natural hair dyes for [latex]$38[/latex] from a beauty supply wholesaler. If the owner plans to double the price before selling it to customers, what is the mark-up rate?

The next question refers to profit, which, in this case, is the same as mark-up amount.

### TRY IT

Mark-up is one type of **percent of change** problem. In the next video we show an example of how to calculate the percent increase of a salary, which is similar to the process of marking-up the price of an item.