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Let the 2 unknown numbers be x and y.

25 + x = 61 => x = 61 – 25 = 36
25 + y = 71 => y = 71 – 25 = 46 #

46 is the largest number.

x + y = 82 (unnecessary fact, but can be used to check answer)

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Thanks Chiefkiasu! 

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