Worked examples
The questions the video works, written out: the setup, each step, the answer and the trap.
0:29Example 1
A $50 shirt is marked up 20%. The next week, that new price is marked down 20%. What is the final price?
- Turn each percent into a multiplier. Up 20% means the price becomes 100% + 20% = 120% of itself, so multiply by 1.20. Down 20% means 100% - 20% = 80% of itself, so multiply by 0.80.
- First change: . The shirt is $60 after the markup.
- Second change, applied to the new price and not the original: .
- Or chain the multipliers first: , and . A multiplier of 0.96 is a 4% loss overall.
- Check: 48 is 12 less than 60, and 12 is 20% of 60. Going up, 60 is 10 more than 50, and 10 is 20% of 50.
Answer: $48, a 4% loss overall
The two percents act on different numbers: the 20% up is taken from $50, but the 20% down is taken from $60, which is bigger, so the cut is worth more dollars than the raise. Most students answer $50 by adding +20% and -20% to get zero change; the SAT counts on exactly that. Percents chain by multiplying, never by adding.
0:47Example 2
After a 25% discount, a jacket costs $60. What was the original price?
- Name the unknown. Let the original price be p. A 25% discount leaves 75% of the price, so the sale price is .
- Set that equal to what the jacket costs now: .
- Undo the multiplication by dividing, not by adding the percent back: .
- Check: 25% of 80 is 20, and 80 - 20 = 60.
Answer: $80
The discount was 25% of the original $80, not 25% of the sale price, so the only way back is to divide by the multiplier that produced the $60. The trap answer is $75, from adding 25% of $60 back on (); test it and it fails, since 25% off $75 is $56.25, not $60.
1:03Example 3
A town of 200 people grows 10%, then shrinks 10%. What is the final population?
- Multipliers: up 10% is , down 10% is .
- , then .
- Chained: , so the town ends at 99% of where it started, a 1% net loss.
- Check: 10% of 220 is 22, and 220 - 22 = 198.
Answer: 198 people
Same shape as the shirt: the 10% shrink is taken from 220, a bigger number than the 200 the growth was taken from, so the town ends below where it began. The trap answer is 200, from cancelling +10% against -10%. An up-then-down pair of equal percents always lands a little below the start.
Lesson transcript
The narration of the video, word for word, under its chapter headings.
Welcome to SAT Climb. Today: percent change — the topic that looks like easy arithmetic and quietly trips up more students than hard algebra. Learn one idea, and these become free points. A $50 shirt goes up 20%, then down 20%. Most students say fifty. The SAT is counting on exactly that. Never add percents. Turn each one into a multiplier. Up 20% means times 1.2. Down 20% means times 0.8. Multiply them together: 0.96. $50 becomes $48 — a 4% loss, not a wash. The same trick runs in reverse. After 25% off, a jacket costs $60. Don't add 25% back — divide. $60 ÷ 0.75 is $80. The original price was $80. If you got 198, you're already thinking in multipliers. Three traps. Adding percents instead of multiplying. Taking the percent of the wrong number. And un-doing a discount by adding it back. Sidestep these three, and percent change is automatic. Percent change: solved. Next lesson: how exponential growth hides in plain sight. Start your free trial at satclimb.com — your SAT is closer than you think.
Read the written version: the Percentages strategy guide, then try 25 hard Percentages questions with full explanations. Both are free, no account needed.