Lesson 6: Discounts and Markups

Property

If the discount on an item is $d\%$, then the sale price for an item originally priced at $S$ dollars will be:

Alternatively, if an item has a $d\%$ discount, you pay $(100-d)\%$ of the original price.

Examples

• A shirt priced at 40 dollars has a 25% discount. The sale price is $40 - \frac{25}{100}(40) = 40 - 10 = 30$ dollars.
• A video game is 15% off its original price of 60 dollars. The new price is $60 - \frac{15}{100}(60) = 60 - 9 = 51$ dollars.
• Using the alternative method, a 30% discount on a 200 dollar bicycle means you pay 70% of the price. The sale price is $0.70 \times 200 = 140$ dollars.

Explanation

A discount lowers the price. You can find the new price by subtracting the discount amount from the original price, or by calculating the percentage of the price you still have to pay.

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.