Finding the Original Cost/Price & Mixed Percent Word Problems

A discount is a reduction in the price of a product or service, usually expressed as a percentage of the original price.

To find the original price, divide the sale price by (1 - discount rate). For example, if the sale price is $575 and the discount is 30%, the original price is $575 / (1 - 0.30) = $821.43.

Sales tax is a percentage added to the sale price of goods and services, collected by the seller and paid to the government.

To find the price before tax, divide the total price by (1 + sales tax rate). For example, if the total price is $8.63 and the sales tax is 8%, the price before tax is $8.63 / (1 + 0.08) = $7.99.

A mixed percent problem involves multiple percentage calculations, such as applying successive discounts or calculating tax on a discounted price.

You pay 70% of the original price after a 30% discount.

To find the final price after multiple discounts, apply each discount sequentially to the price after the previous discount.

Amount saved = Original price x Discount rate. For example, if the original price is $6.67 and the discount is 45%, the amount saved is $6.67 x 0.45 = $3.

The original price is $8.10 / (1 - 0.10) = $9.00.

Final price = Sale price x (1 - discount rate). For example, if the sale price is $154.50 and the discount is 70%, the final price is $154.50 x (1 - 0.70) = $46.35.