Worked examples: from question to answer
Use these walkthroughs to check your own calculations and understand the correct base.
Example 1: Sale price and tax
Question: A $160 jacket is 30% off, with 7% sales tax on the discounted price.
Discount: $160 × 0.30 = $48. Sale price: $160 − $48 = $112. Tax: $112 × 0.07 = $7.84. Final: $119.84.
Example 2: Raise versus salary
Question: A monthly salary changes from $4,000 to $4,300.
Difference: $300. Percent increase: $300 ÷ $4,000 × 100 = 7.5%.
Example 3: Reverse a discounted price
Question: The sale price is $68 after a 15% discount.
Remaining proportion: 0.85. Original = $68 ÷ 0.85 = $80.
Example 4: Profit margin versus markup
Question: An item costs $45 and sells for $75.
Profit = $30. Margin = $30 ÷ $75 = 40%. Markup = $30 ÷ $45 = 66.67%.
Example 5: Compounding a decrease
Question: A $500 value falls 10% in each of two periods.
After period one: $450. After period two: $405. Overall change: −$95 or −19%, not −20%.
Example 6: Percentage points
Question: A rate moves from 2% to 3%.
The increase is one percentage point, while the relative increase is (3−2) ÷ 2 × 100 = 50%.
Example 7: Tip and split
Question: A $96 bill has a 20% tip and is split among four people.
Tip = $19.20. Total = $115.20. Each share = $28.80.