Mathematics
Grade 6
15 min
Sale prices: find the original price
Sale prices: find the original price
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1
Introduction & Learning Objectives
Learning Objectives
Identify the components of a sale price problem: sale price, discount percentage, and original price.
Convert percentages to decimals or fractions for use in calculations.
Formulate an algebraic equation to represent the relationship between original price, sale price, and discount percentage.
Solve one-step algebraic equations to find an unknown original price.
Apply the concept of inverse operations to reverse a discount calculation.
Verify the calculated original price by applying the discount to it.
Explain why the discount is applied to the original price, not the sale price.
Ever wonder how stores figure out the original price of an item when it's on sale? 🕵️♀️ Let's become math detectives and uncover those hidden original prices!
In t...
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Key Concepts & Vocabulary
TermDefinitionExample
Original PriceThe initial, full price of an item before any discounts or sales are applied.A new video game costs $60 before any sale.
Sale PriceThe reduced price of an item after a discount has been applied.The video game is on sale for $48.
DiscountThe amount of money subtracted from the original price.The discount on the video game is $12 ($60 - $48).
Discount Rate (or Discount Percentage)The percentage by which the original price is reduced.If the $60 video game is on sale for $48, the discount is $12. The discount rate is ($12 / $60) * 100% = 20%.
PercentageA way to express a part of a whole as a fraction of 100. It is often written with the '%' symbol.20% means 20 out of 100, or 0.20 as a decimal.
Algebraic ExpressionA mathematical phrase that can con...
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Core Formulas
Calculating Discount Amount
`Discount Amount = Original Price \times Discount Rate`
This rule helps you find the actual dollar amount saved if you know the original price and the percentage discount. Remember to convert the discount rate to a decimal or fraction.
Sale Price from Original Price and Discount Rate
`Sale Price = Original Price \times (1 - Discount Rate)`
This rule shows that if an item is, for example, 25% off, you are paying 75% (100% - 25%) of the original price. Convert the discount rate to a decimal before subtracting from 1.
Finding the Original Price (Core Formula)
`Original Price = \frac{Sale Price}{(1 - Discount Rate)}`
This is the key formula for our lesson. It allows you to work backward from the sale price and discount rate to find the origina...
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Challenging
A customer buys a discounted television for $350. The discount was 30%. The customer then has to pay a separate $20 delivery fee. What was the original price of the television BEFORE the discount and delivery fee?
A.$481
B.$520
C.$500
D.$455
Challenging
A winter coat is marked down by 20%. Because it doesn't sell, it is discounted by an additional 10% off the new sale price. If the final price is $72, what was the original price before any discounts?
A.$99
B.$100
C.$108
D.$96
Challenging
An item's sale price is exactly 60% of its original price. What was the discount percentage, and if the sale price is $30, what was the original price?
A.40% discount; original price was $50.
B.60% discount; original price was $75.
C.40% discount; original price was $48.
D.60% discount; original price was $50.
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