These questions ask for a saving, an added charge or the amount paid after one or more percentage changes. The main decision is whether you need the percentage part by itself or a final total that still includes the starting amount.
Choose the quantity before calculating
First underline what is requested: the discount, the tax or tip, or the final price. Convert p% to p/100. For the percentage part alone, multiply the relevant base by p/100. For a final amount after a discount, multiply by 1 - p/100. For a final amount after an added charge, multiply by 1 + p/100.
| Signal in the question | Form to use |
|---|---|
| Saving, tax, tip or charge alone | base × p/100 |
| Price after p% off | original price × (1 - p/100) |
| Total after p% is added | starting amount × (1 + p/100) |
| Several percentage changes | starting amount × first multiplier × next multiplier |
For example, a 20% discount on 74 dollars leaves 80%, so the price is 74 × 0.80 = 59.20 dollars. A 15% added charge on 52 dollars gives 52 × 1.15 = 59.80 dollars, whereas the charge alone is 52 × 0.15 = 7.80 dollars.
When changes happen one after another, update the base at every step. An item priced at 90 dollars with 20% off and then 5% tax becomes 90 × 0.80 × 1.05 = 75.60 dollars. The tax is applied to the discounted price. Multiplying the two factors is enough; reversing their order gives the same product, although the story still determines what each factor means.
Common traps
| Tempting route | How to reject it |
|---|---|
| Using p/100 when the question asks for the full amount after a charge | That calculation finds only the amount added. Use 1 + p/100 when the starting amount must remain in the total. |
| Subtracting a tip or service charge | A charge is an increase, so its final multiplier is greater than 1. A multiplier below 1 belongs to a reduction. |
| Adding or subtracting successive rates to make one net rate | The later percentage uses an updated base. Write one multiplier for each change and multiply them instead. Equal decrease and increase rates do not cancel. |
| Stopping after the discount when another charge follows | The discounted amount is only an intermediate value. Check the wording for every later change before treating it as final. |
| Subtracting the percentage number as though it were a money amount | A rate has no dollar value until it is multiplied by its base. Find p/100 of the price before subtracting the saving. |
Try it
A pair of shoes costs 80 dollars before a 25% discount. What is the sale price? Enter the amount in dollars.
A cafe bill is 36 dollars. What is the amount of an 18% tip? Enter the amount in dollars.
A concert ticket costs 125 dollars before a 16% service charge. What is the total after the charge? Enter the amount in dollars.