## 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.

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. | |

Simplify. | |

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. | |

Simplify. | |

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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