Problem 16 · 2009 Math Kangaroo
Stretch
Algebra & Patterns
custom-operationsubstitution
If a ◯ b = ab + a + b and 3 ◯ 5 = 2 ◯ x, then x equals
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Answer: C — 7
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Hint 1 of 2
The rule a∘b = ab + a + b is just a recipe — plug numbers straight in.
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Hint 2 of 2
Compute 3∘5 first, then solve 2∘x for x.
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Approach: apply the defined operation to both sides
- 3∘5 = 3·5 + 3 + 5 = 23.
- 2∘x = 2x + 2 + x = 3x + 2, and this must equal 23.
- So 3x + 2 = 23, giving x = 7.
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