2.1: Mark-Up Problems

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Learning OUTCOME

Use mathematical notation to solve markup problems

Image of two gold earrings made of tiny white, purple, and pink beads. — 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.
[reveal-answer q=”661316″]Show Answer[/reveal-answer]
[hidden-answer a=”661316″]

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 $40\text{%}$ of the wholesale price.
Translate into an equation.
Simplify.	$m=100$
Check if this answer is reasonable.
Yes. The markup rate is less than $50\text{%}$ and $\text{\$100}$ is less than half of $\text{\$250}$.
Write a complete sentence that answers the question.	The mark-up on the photograph was $\text{\$100}$.

ⓑ
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.	$p=350$
Check if this answer is reasonable.
Yes. The list price, $\text{\$350}$, is more than the wholesale price, $\text{\$250}$.
Write a complete sentence that answers the question.	The list price of the photograph was $\text{\$350}$.

[/hidden-answer]

try it

[ohm_question hide_question_numbers=1]146778[/ohm_question]

TRY IT

[ohm_question hide_question_numbers=1]978[/ohm_question]

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?

[reveal-answer q=”664216″]Show Answer[/reveal-answer]
[hidden-answer a=”664216″]

Solution

If Braided Salon purchases the hair dye for $$38$, they will charge customers $$56$$(2 \cdot $38 = $56)$. The mark-up in this case is the difference between the final price tag and the wholesale cost: $$56 - $38 = $38$.

amount of mark-up = mark-up rate $\cdot$ wholesale price

$$38 = x \cdot $38$

$x = 1$

$1 = 100%$

The mark-up rate is $100%$ when doubling the wholesale cost.

[/hidden-answer]

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

TRY IT

[ohm_question hide_question_numbers=1]154749[/ohm_question]

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.

Thumbnail for the embedded element "Example 2: Determine a Percent of Change (increase)"

A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/afm-2/?p=106

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