Problem 4 · 2026 AMC 8
Medium
Fractions, Decimals & Percents
percent-multiplier
Brynn's savings decreased by 20% in July, then increased by 50% of the new amount in August. Brynn's savings are now what percent of the original amount?
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Answer: E — 120%.
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Hint 1 of 2
Careful — the answer isn't simply −20 + 50 = +30%. The 50% rise acts on the already-shrunk amount, so the two changes don't just add.
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Hint 2 of 2
Turn each change into a multiplier (×0.8, then ×1.5) and multiply them — that's how percent changes compound, and you never need the starting amount.
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Approach: turn each percent change into a multiplier
- A percent change is really a multiplier: down 20% leaves 80%, so × 0.8; up 50% means × 1.5. And changes chain by multiplying, so you never need a starting amount.
- 0.8 × 1.5 = 1.2, which is 120% of the original.
- Watch the trap: the answer is not −20% + 50% = +30%. Percents stack by multiplying, not adding, because the +50% applies to the shrunken amount, not the original.
Another way — plug in a friendly number:
- Pretend Brynn started with $100. July: down 20% leaves $80. August: up 50% of $80 adds $40, giving $120.
- $120 out of the original $100 is 120%. Picking 100 makes the percent fall right out.
Mark:
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