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Solving Mark-up Applications

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Solving Mark-up Applications

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.

Definition: Mark-up

The mark-up is the amount added to the wholesale price.

\(\begin{array}{ccc}\hfill \text{amount of mark-up}& =& \text{mark-up rate}·\text{wholesale price}\hfill \\ \hfill \text{list price}& =& \text{wholesale price}+\text{mark up}\hfill \end{array}\)

The list price should always be more than the wholesale price.

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% of the wholesale price.
Translate into an equation.Solving Mark-up Applications
Simplify.Solving Mark-up Applications
Check if this answer is reasonable. 
Yes. The markup rate is less than 50% and \$100 is less than half of \$250. 
Write a complete sentence that answers the question.The mark-up on the photograph was \$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.Solving Mark-up Applications
Simplify.Solving Mark-up Applications
Check if this answer is reasonable. 
Yes. The list price, \$350, is more than the wholesale price, \$250. 
Write a complete sentence that answers the question.The list price of the photograph was \$350.

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