Problem 19 · 2020 Math Kangaroo
Stretch
Algebra & Patterns
substitutiondivisibility
Let \(17x + 51y = 102\). If x and y are strictly positive integers, what is the value of \(x - 3y\)?
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Answer: B — 0
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Hint 1 of 2
Divide the whole equation by the common factor to simplify it.
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Hint 2 of 2
From the simplified relation, write x in terms of y and find the only positive solution.
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Approach: reduce the equation and solve over positive integers
- Dividing 17x + 51y = 102 by 17 gives x + 3y = 6.
- Strictly positive integers force y = 1, x = 3.
- Then x − 3y = 3 − 3 = 0.
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