Key takeaway: A discount is an amount taken off the regular price of an item, often stated as a percent of that price, so the sale price equals the regular price minus the discount.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Discount
A discount is a reduction in price. Stores offer one to clear shelves, reward loyal customers or attract shoppers during a holiday weekend.
When the reduction is given as a percent, it is a percent of the regular price, so a bigger price produces a bigger saving in dollars. Two numbers are worth finding: the amount saved, and the sale price that you actually pay. The sale price is always smaller than the regular price, unless the percent is 0.
Formula and notation
With the rate \(r\) written as a decimal:
\[\text{amount saved} = r \times \text{regular price}, \qquad \text{sale price} = \text{regular price} – \text{amount saved}\]
A shortcut is \(\text{sale price} = \text{regular price} \times (1 – r)\). For “35% off”, multiply by \(0.65\).
Key facts
- A 35% discount means you pay the other 65% of the regular price.
- The percent off is always figured on the regular price, before any tax is added.
- Two successive discounts are not the same as one discount equal to their sum.
- The amount saved plus the sale price always equals the regular price.
Discount example
A pair of hiking boots has a regular price of \$84.00 at an outdoor store in Boise. This weekend every pair is 35% off. Find the amount saved and the sale price.
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Change 35% to a decimal: \(35\% = 0.35\).
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Amount saved: \(0.35 \times 84 = 29.40\).
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Sale price: \(84.00 – 29.40 = 54.60\).
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Check with the shortcut: \(0.65 \times 84 = 54.60\).
The shopper saves \$29.40 and pays \$54.60.
Common mistake
Watch out
A rack shows “20% off, then take an extra 10% off.” Tariq says the boots are 30% off, so a \$50 jacket costs \$35.
Why it is wrong
The second percent applies to the already reduced price. After 20% off, the jacket costs \(0.80 \times 50 = 40\) dollars. Taking 10% off that gives \(0.90 \times 40 = 36\) dollars. The true saving is 28%, so the jacket is \$36, not \$35.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents