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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \(b - 3 = 7\)

📌 \(b - 3 = -7\)

📌 Solve each equation:

📌 \(b - 3 = 7 \Rightarrow b = 10\)

📌 \(b - 3 = -7 \Rightarrow b = -4\)

📌 The sum of all solutions is:

📌 + (-4) = 6

📌 Thus, the sum of all values of \(b\) is \(\boxed{6}\).Question: A cartographer is designing a grid-based map system where two roads intersect at a point, represented by positive integers \(a\) and \(b\), such that the total length of the combined road segments is 1000 units. If the greatest common divisor of \(a\) and \(b\) determines the largest uniform segment size that fits both roads exactly, what is the largest possible value of \(\gcd(a, b)\)?

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