A percent is a rate per hundred. SAT percentage problems often test the choice of base: the original amount is the denominator for percent change, while a final amount may require working backward through a multiplier.
Essential concepts
\[ ext{new}= ext{original}(1pm r) qquad % ext{ change}= rac{ ext{change}}{ ext{original}} imes100%\]
Use decimal r, so 15% becomes 0.15.
SAT strategy and application
Calculate a discounted price
An $80 item is discounted by 15%. What is the sale price?
- Find the remaining multiplier
\(1-0.15=0.85\).
- Apply it to the original price
\(80(0.85)=68\).
Sale price: $68.
Mistakes and traps
Check your understanding
A value rises from 50 to 65. What is the percent increase?
- 15%
- 23%
- 30%
- 65%
Show answer and explanation
Answer: 30%
The increase is \(15\), and \(15/50=0.30\).
Key takeaways
What to remember
- Identify the original reference amount before calculating.
- Use multipliers for increases, decreases, and repeated changes.
- Divide by a multiplier when solving backward from a final amount.
- Do not add sequential percentage changes unless the bases are identical.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.