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

Emily multiplied two integers together. Her answer was 360. Finley increased each of Emily's integers by one and then multiplied the two new integers together. His answer was 400. What was the sum of Emily's two integers?

(A) $39$ (B) $40$ (C) $42$ (D) $45$ (E) $48$

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