# 2.1: Mark-Up Problems

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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 $$18$$. 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.

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 $$\text{\350}$$.

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?

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.

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.

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