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 [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.

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.

Show Answer

Solution

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

ⓑ
Identify what you are asked to find.	What is the list price?
Choose a variable to represent it.	Let [latex]p=[/latex] 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.	[latex]p=350[/latex]
Check if this answer is reasonable.
Yes. The list price, [latex]\text{\$350}[/latex], is more than the wholesale price, [latex]\text{\$250}[/latex].
Write a complete sentence that answers the question.	The list price of the photograph was [latex]\text{\$350}[/latex].

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

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.