Problem 8 · 2025 Math Kangaroo
Easy
Algebra & Patterns
sum-constraintsubstitution
Luka has dogs, rabbits and cats as pets. Eight of these pets are not dogs, five of these pets are not rabbits and seven of these pets are not cats. How many pets does Luka have?
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Answer: A — 10
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Hint 1 of 2
Let the counts of dogs, rabbits, cats be d, r, c and turn each 'not' statement into an equation.
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Hint 2 of 2
Add the three equations; each total counts every pet twice.
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Approach: set up and add the three equations
- Not dogs: r+c=8; not rabbits: d+c=5; not cats: d+r=7.
- Adding: 2(d+r+c) = 20, so d+r+c = 10.
- Luka has 10 pets.
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