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2010 Math Kangaroo

Problem 20

Problem 20 · 2010 Math Kangaroo Hard
Algebra & Patterns substitution

Which of the numbers a, b, c, d, and e is biggest if \(a - 1 = b + 2 = c - 3 = d + 4 = e - 4\)?

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Answer: Ee
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Hint 1 of 2
Set the common value to k and write each letter in terms of k.
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Hint 2 of 2
Whoever has the largest added shift is biggest.
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Approach: express all five in terms of the common value
  1. Let the shared value be k: a = k+1, b = k−2, c = k+3, d = k−4, e = k+4.
  2. The largest is the one with the biggest offset, +4, which is e.
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