Percent Applications: Discount, Tax, Tip

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Skill: percent-applications

Percent Applications: Discount, Tax, Tip

Almost every number that touches your wallet is a percent. A discount subtracts a percent of the price, sales tax and tips add one, percent change compares a new value to the old one, and simple interest grows money over time.

1 Understand

The four jobs percents do in real life.

What it is

“Percent” means “per hundred” — 25% is 25/100 = 0.25. Percent applications are the real-world jobs percents do: a discount subtracts a percent of the price, sales tax and tips add one, percent change compares a new value to the old one (change ÷ original), and simple interest grows money over time.

Why it matters

Almost every number that touches your wallet is a percent. Reading a sale tag, splitting a restaurant bill, or judging whether a “50% bigger!” claim is honest all run on these four moves.

Where it is used

Sale prices and coupons · restaurant tips · sales tax · investment growth · test-score improvements.

2 See It

Every percent is a slice of 100 — and “percent off” plus “percent paid” always add to 100%.

Every percent is a slice of 100. A 35% discount removes 35 of these 100 slices from the price.
$80 jacket 25% OFF discount $20 sale price $60 25% off + 75% paid = 100%
25% of $80 is $20 off — you pay the other 75%, which is $60. Percent off and percent paid always add to 100%.

3 Worked Examples

Four moves: discount, tax, percent change, tip. Same percent engine underneath each one.

Example 1 Discount: $80 jacket, 25% off
  1. Thinking: discount = percent × price = 0.25 × 80 = $20. Sale price = 80 − 20.
  2. Discount = 0.25 × $80 = $20.00.
  3. Sale price = $80.00 − $20.00 = $60.00.
Sale price = $60.00. Check: you are paying 75%: 0.75 × 80 = $60. Matches.
Example 2 Sales tax: $45 meal, 8% tax
  1. Thinking: tax = 0.08 × 45 = $3.60. Total = 45 + 3.60.
  2. Tax = 0.08 × $45 = $3.60.
  3. Total = $45.00 + $3.60 = $48.60.
Total = $48.60. Check: 8% of ~$45 is about $3.60 — the total is sensibly just above $45.
Example 3 Percent change: price rises from $50 to $65
  1. Thinking: change = 65 − 50 = $15. Percent change = change ÷ original = 15/50 = 0.30.
  2. Change = $65 − $50 = $15.
  3. Percent change = $15 ÷ $50 = 0.30 = 30% increase.
30% increase. Check: 30% of $50 is $15, and $50 + $15 = $65. Matches.
Example 4 Tip: $60 bill, 15% tip
  1. Thinking: tip = 0.15 × 60 = $9. Total = 60 + 9.
  2. Tip = 0.15 × $60 = $9.00.
  3. Total = $60.00 + $9.00 = $69.00.
Tip $9.00, total $69.00. Check: 10% is $6 and 5% is $3, so 15% = $9. The 10% + 5% split is the fastest mental-tip trick.

4 Common Mistakes

The three traps that catch even strong students. Learn them here, not at the register.

Mistake 1: dividing percent change by the NEW value
Wrong
$50 → $65: “15/65 ≈ 23%”
Right
change ÷ original = 15/50 = 30%.
Rule: percent change always asks “compared to where we started?” — the original is the denominator.
Mistake 2: computing tax on the original price instead of the sale price
Wrong
$80 jacket, 25% off, 8% tax → tax = 0.08 × 80 = $6.40.
Right
tax applies to what you actually pay: 0.08 × 60 = $4.80.
Rule: follow the real-world order — discount first, then tax on the discounted price. You do not pay tax on money you never spend.
Mistake 3: thinking “30% off, then 30% back on” returns to the original
Wrong
$100 → $70 → “add 30% of 70 = $21” → $100 claimed.
Right
0.70 × 1.30 = 0.91 — you land at $91, not $100.
Memory hook: percents don’t “undo” — the second percent acts on a different base.

5 Quick Check

Try each one on paper first, then reveal the answer.

1. A $120 pair of shoes is 30% off. What is the sale price?
Answer
Discount = 0.30 × 120 = $36.00; sale price = $120 − $36 = $84.00. (Or: pay 70% → 0.70 × 120 = $84.)
2. A stock price goes from $40 to $52. What is the percent increase?
Answer
Change = $12; $12 ÷ $40 = 0.30 = 30% increase. (Divide by the original $40, not the new $52.)
3. A store raises a $60 item by 25%, then discounts the new price by 20%. What is the final price?
Answer
$60 × 1.25 = $75; $75 × 0.80 = $60.00 — back where it started! (A coincidence of these numbers, not a rule.)

Key Points to Remember

  • Discount: find p% of the price, then subtract. Or pay (100−p)% directly.
  • Tax and tip: find p% of the base, then add. Tax goes on the sale price.
  • Percent change = change ÷ original — never the new value.
  • Successive percents multiply: +25% then −20% is ×1.25 ×0.80. They never simply add or undo.
  • Simple interest = principal × rate × time.
Practice percent applications Try the calculators Explore the lab
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