2.1: Mark-Up Problems
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.
[reveal-answer q=”661316″]Show Answer[/reveal-answer]
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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.
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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.