Problem 10 · 2013 Math Kangaroo
Easy
Number Theory
Algebra & Patterns
factorization
For the positive whole numbers x, y, z the following is true: x×y = 14, y×z = 10 and z×x = 35. What is the value of x + y + z?
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Answer: C — 14
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Hint 1 of 2
Multiply all three equations together to get (xyz) squared.
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Hint 2 of 2
Once you know xyz, divide by each product to recover one variable at a time.
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Approach: multiply the equations
- (xy)(yz)(zx) = (xyz)² = 14 × 10 × 35 = 4900, so xyz = 70.
- x = xyz / yz = 70/10 = 7, y = 70/35 = 2, z = 70/14 = 5.
- x + y + z = 7 + 2 + 5 = 14.
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