Problem 24 · 2014 Math Kangaroo
Stretch
Fractions, Decimals & Percents
ratiopercent-multiplier
On an island the frogs are either green or blue. The number of blue frogs increases by 60%, and the number of green frogs decreases by 60%. As a result, the new ratio of blue frogs to green frogs equals the original ratio of green frogs to blue frogs. By what percentage has the total number of frogs changed?
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Answer: B — 20%
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Hint 1 of 2
Set up the new blue-to-green ratio equal to the old green-to-blue ratio.
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Hint 2 of 2
That equation pins the original green-to-blue ratio; then compare totals.
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Approach: solve the swapped-ratio equation, then compare totals
- With blue B, green G: 1.6B / 0.4G = G / B leads to 4B² = G², so G = 2B.
- Old total 3B; new total 1.6B + 0.4(2B) = 2.4B, a drop of 0.6B.
- The total changes by 0.6B / 3B = 20% (a decrease).
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