Problem 30 · 2022 Math Kangaroo
Stretch
Algebra & Patterns
substitutionsum-constraint
Altogether 2022 kangaroos and some koalas live in seven parks. In each park there live as many kangaroos as there are koalas in all the other parks together. How many koalas live in the seven parks in total?
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Answer: B — 337
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Hint 1 of 2
Kangaroos in each park equal the koalas in all the OTHER parks; add this up over the seven parks.
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Hint 2 of 2
Let total koalas be K; summing kangaroos over parks gives 7K minus K. Set that equal to 2022.
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Approach: sum the cross-park condition
- Let the total number of koalas be K. In each park the kangaroos equal K minus that park's own koalas.
- Summing over all seven parks: total kangaroos = 7K - K = 6K = 2022.
- So K = 337 koalas in total, the answer is B.
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