Sale prices: find the original price

Learning Objectives Define key terms related to sale prices and original prices. Identify the relationship between original price, sale price, and discount percentage. Set up and solve linear equations to find the original price of an item given its sale price and discount rate. Use proportions to determine the original price of an item. Apply the formula for finding the original price to real-world scenarios. Accurately calculate the original price of an item after a percentage discount. Explain common errors when calculating original prices and how to avoid them. Ever wonder if you're getting the best deal, or what something *really* cost before that big '25% OFF!' sign? 🏷️💰 Let's become shopping detectives! In this lesson, you'll learn how to...

TermDefinitionExample Original PriceThe initial, full, or regular price of an item before any discounts or sales are applied.A shirt that normally costs $20 has an original price of $20. Sale PriceThe reduced price of an item after a discount has been applied.If a $20 shirt is 25% off, its sale price is $15. DiscountThe amount of money subtracted from the original price, usually expressed as a percentage or a fixed dollar amount.For a $20 shirt with a $5 discount, the discount is $5. Discount Rate (or Percentage Discount)The percentage by which the original price is reduced.If a $20 shirt is on sale for $15, the discount is $5, and the discount rate is ($5/$20) * 100% = 25%. PercentageA way of expressing a number as a fraction of 100, often represented by the symbol '%'.25% mean...

Relationship between Prices and Discount $$ \text{Sale Price} = \text{Original Price} - \text{Discount} $$ This rule shows that the sale price is what's left after the discount amount is taken off the original price. The discount itself is a percentage of the original price. Finding Original Price using Percentage Remaining $$ \text{Original Price} = \frac{\text{Sale Price}}{1 - \text{Discount Rate (as a decimal)}} $$ This is the primary formula for finding the original price. The sale price represents the percentage of the original price that is *left* after the discount. For example, if there's a 20% discount, the sale price is 80% (1 - 0.20) of the original price. Finding Original Price using Proportions $$ \frac{\text{Sale Price}}{\text{Original Price}} =...