Problem 19 · 2025 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
Emus, snakes and kangaroos live together on an Australian farm. Emus have two legs and no tail. Kangaroos have four legs and a tail. Snakes have no legs but a tail. Every animal has two eyes. Altogether they have 18 eyes, 7 tails and 24 legs. How many kangaroos live on the farm?
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Answer: E — 5
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Hint 1 of 2
Every animal has 2 eyes, so the eye count gives the total number of animals.
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Hint 2 of 2
Use tails to split snakes+kangaroos from emus, then legs to isolate the kangaroos.
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Approach: set up and solve from eyes, tails and legs
- 18 eyes mean 9 animals; 7 tails are carried by kangaroos and snakes, so 2 emus.
- Legs: emus give 2×2 = 4, so kangaroos give 24 − 4 = 20 legs.
- Each kangaroo has 4 legs, so there are \(20 \div 4 = 5\) kangaroos, which is (E).
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