Problem 18 · 2013 Math Kangaroo
Hard
Algebra & Patterns
substitution
Matthias is catching fish. If he had caught three times as many fish as he actually has, he would have 12 more fish. How many fish has he caught?
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Answer: B — 6
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Hint 1 of 3
Three times the catch is the real catch counted three times over.
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Hint 2 of 3
Going from one catch to three catches adds two more catches, and that extra is the 12.
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Hint 3 of 3
So two catches make 12; cut that in half to get one catch.
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Approach: see the extra fish as two more catches
- Three times the catch is the catch plus two extra copies of the catch.
- Those two extra copies are the 12 more fish, so two catches equal 12.
- One catch is half of 12, which is 6, so he caught 6 fish, choice B.
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