Lesson 5: Solve Markup and Markdown Problems

Property

The formulas for calculating a mark-up are:

Keep in mind that the list price should always be more than the original cost.

Examples

• An art gallery buys a sculpture for 400 dollars and marks the price up by 60%. What is the amount of mark-up and the list price?

The amount of mark-up is $0.60 \times 400 = 240$ dollars. The list price is $400 + 240 = 640$ dollars.

• A music store buys a guitar for 1,500 dollars and sells it for 2,100 dollars. What is the amount of mark-up and the mark-up rate?

The amount of mark-up is $2100 - 1500 = 600$ dollars. To find the rate, solve $600 = r \cdot 1500$, which gives $r = 0.4$, or a 40% mark-up rate.

Property

An amount of discount is a percent off the original price.

Property

Markup in the retail industry means the percentage of cost for an item that is added to set the sale price of the item. If the markup is $m\%$, then the sale price for an item costing $C$ dollars will be:

Examples

• A bookstore buys a novel for 10 dollars and applies a 40% markup. The sale price is $10 + \frac{40}{100}(10) = 10 + 4 = 14$ dollars.
• A toy store's cost for a doll is 25 dollars. With a 20% markup, the customer price is $25 + \frac{20}{100}(25) = 25 + 5 = 30$ dollars.
• An electronics store uses a 15% markup on headphones that cost 80 dollars. The sale price becomes $80 + \frac{15}{100}(80) = 80 + 12 = 92$ dollars.

Explanation

Markup is how stores make a profit. They buy an item at a cost price and add a percentage on top to get the selling price. This extra amount covers their expenses and earnings.