## Mark-Up Problems

### Learning OUTCOME

• Use mathematical notation to solve markup problems

Blue Boat Design Earrings

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

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 $\cdot$ 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 $100\%$.

### 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.

### 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 $38$ 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.

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