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Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Harriet writes a positive integer on each edge of a square. She also writes at each vertex the product of the integers on the two edges that meet at that vertex. The sum of the integers at the vertices is 15. What is the sum of the integers on the edges of the square?

(A) $6$ (B) $7$ (C) $8$ (D) $10$ (E) $15$

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