Percent in the wild.
Tip, sales tax, raises, discounts, markup. Different stories, same recipe. This lesson teaches you the move and the one-step shortcut that pays off all term.
Friday night: $48 dinner with four people, you put in a 20% tip. Saturday: a $80 jacket 25% off. Monday: a $200 grocery run plus 6% sales tax.
Three different scenarios, one recipe. Tip, sale, and tax are all just percent on or percent off a base price. By the end of this lesson you'll have a one-step shortcut for both directions.
On vs. off: same recipe, two directions.
Same $80 base, two directions: 25% off lands at $60, 20% on lands at $96.
A percent change is a percent of a base, added to or subtracted from that base. Percent on = base + (rate × base). Percent off = base − (rate × base).
The vocabulary you'll see in word problems
- Markup An increase added to a base price. A store buys an item for $20, marks it up 50%, and sells it for $30.
- Discount A decrease taken off a base price. A $60 sweater on sale at 30% off costs $42.
- Tip A percent added to a restaurant bill, usually 15%-20% in the U.S. Math is the same as sales tax.
- Sales tax A percent added to a purchase price by the state or city. Rates vary, often between 5% and 9%.
- Percent change The catch-all term for any move that increases or decreases a base by a percent. ALEKS uses this language often.
- Combined factor The single multiplier that applies two (or more) percent moves at once. 25% off then 7% tax = 0.75 × 1.07 = 0.8025. Multiply the base by that and you're done — two moves, one cell.
- Order of operations (percents) When stacking discounts and tax, the discount applies to the original price; tax then applies to the already-discounted price. Doing them in the wrong order changes the final total.
$80 jacket, 25% off, plus 7% sales tax.
"You grab an $80 jacket on sale at 25% off. At the register, sales tax is 7%. What's the final total?"
Compute the discount amount.
The discount is 25% of the original price. Convert 25% to a decimal (0.25), then multiply by $80.
Subtract the discount from the base.
Sale price = original − discount.
Compute the sales tax (on the sale price).
Sales tax applies to the sale price, not the original. 7% of $60.
Add the tax to get the total.
Final = sale price + tax.
Sanity check.
Original was $80. Discount takes it down to $60. Tax adds a few dollars back. The final answer of $64.20 is between $60 and $80, exactly where it should be.
Three problems. One recipe in three flavors.
What's the sales tax on a $50 grocery bill at 6%? (Just the tax amount, not the total.)
Dinner is $36 and you tip 20%. What do you pay total?
A $120 jacket is 25% off, then 7% sales tax is added. What's the final total?
Three fast questions before you move on.
Q1. Which expression gives the same result as adding 20% to a price?
Q2. If you tip 18% on a $40 meal, the tip amount is...
Q3. A $100 item is 25% off. How much do you pay?
The one-step shortcut.
Most percent applications are percent ON or percent OFF a base. Once you spot which direction you're going, multiply by the right combined factor in one step.
In ALEKS, percent-change problems are the heart of Topic 2. Read the prompt twice: is this percent on or percent off? Pick the right multiplier and you'll cut your steps in half.
In Excel, the multiplier shortcut shines. Put the price in cell A2 and the rate in B2, then write =A2*(1+B2) for tax/tip or =A2*(1-B2) for a sale. Same formula scales to a whole budget without re-typing.
Next: Lesson 04 leaves percent behind for unit conversions: feet to meters, ounces to grams, dollars to euros. Different topic, same "multiply by 1 in disguise" trick.
Continue to Lesson 04Different angle? Need another rep? These are optional — tap any that look helpful.
Percent Word Problems: Sales Tax, Discount, & Finding the Original Price
Multiple worked dollar-and-cents examples: sales tax added on, discount taken off, and reverse-engineering original price from a sale price. Matches the lesson's $80-jacket-with-tax flavor exactly.
Tax, discount and tip examples
Sal works real-world tip and tax-and-discount problems, naturally arriving at the multiplier-shortcut intuition (paying 108% of the bill, paying 75% of the price). Different voice from OCT and shorter, good for one more pass before a quiz.