HSPT: Percents: find a price after a discount
Learn to find a sale price quickly by building percents from 10% and 5%, and to avoid stopping at the discount amount.
How do you find what something costs after a percent discount, without a calculator?
Short answer
Find the discount as a percent of the starting price and subtract it. Or multiply the starting price by the percent that is left.
Know first: Multiplying by 10 and dividing by 10, Decimals for money
Step 1 of 5
A discount is a percent of the starting price
A discount is a percent taken off a starting price. Percent means per hundred, so 30% off means 30 dollars off for every 100 dollars of price.
There are two routes to the sale price. Find the discount and subtract it. Or find what is left: 30% off leaves 70%, so multiply the price by 0.7. Both give the same answer.
| Percent | How to find it | Example on $250 |
|---|---|---|
| 10% | Move the decimal point one place left | $25 |
| 5% | Half of 10% | $12.50 |
| 25% | One quarter | $62.50 |
| 50% | One half | $125 |
Build other percents from these: 30% is three 10%s, and 35% is three 10%s plus 5%.
Step 2 of 5
Find the discount, then subtract
Worked example: A jacket at 30% off
A jacket costs $90 before a 30% discount. What is the price after the discount?
- A$27
- B$63
- C$117
- D$60
- 1
Find 10%
10% of $90 is $9.
- 2
Build 30%
3 × $9 = $27. That is the discount.
- 3
Subtract
$90 − $27 = $63.
- 4
Check with the multiplier
30% off leaves 70%, and 0.7 × 90 = 63.
- 5
See why the other choices are there
$27 is the discount, not the price you pay. $117 adds the discount. $60 subtracts 30 dollars instead of 30 percent.
Answer
$63
Find the wrong step
A student finds the price of a $160 bike after a 20% discount.
- 1
Finds 10% of $160: $16.
- 2
Doubles it to get 20%: $32.
- 3
Answers $32.
What went wrong
$32 is the discount. The question asks for the price after the discount, so one more step is needed.
The fix
Subtract the discount: $160 − $32 = $128.
Step 3 of 5
Discount first, then the price you pay
Check yourself · Question 1
Shoes cost $55 before a 20% discount. What is the price after the discount?
Answer: B
10% of $55 is $5.50, so 20% is $11. Subtract: $55 − $11 = $44. Or use the multiplier: 20% off leaves 80%, and 0.8 × 55 = 44.
Trap answer: $11
Stopping at the discount
- Why it looks right
- Finding 20% of $55 is the main calculation, so the result feels like the answer.
- Why it's wrong
- The question asks for the price after the discount. $11 is what you save, not what you pay.
- The right answer
- $44, because $55 − $11 = $44.
Check yourself · Question 2
A game costs $70 before a 35% discount. What is the price after the discount?
Answer: D
35% off leaves 65%, and 0.65 × 70 = 45.50. Or find the discount: 10% is $7, so 30% is $21 and 5% is $3.50, for $24.50 off. Then $70 − $24.50 = $45.50.
Common mistake
"30% off means I subtract 30."
- Why it's tempting
- The number in the question is right there, and subtracting it is quick.
- Do this instead
- A percent is always of something. Find 30% of the price first, then subtract that amount.
Step 4 of 5
What to remember
Remember
- A discount is a percent of the starting price; find it before you subtract.
- Build percents from 10% and 5%, or multiply by what is left, such as 0.7 for 30% off.
- The discount amount is a trap choice when the question asks for the price you pay.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
What was the discount in dollars in the practice question, and which choice was that discount?