Intelligent Question

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Meeting an old friend with two young children, I asked their ages and, being a mathematician, she told me that the product of her age and each of the two children's ages gave the answer 2,450. After a pause for thought, I said 'That gives too many possibilities. What is the sum of your three ages?' 'The same as your age' she said That still left me with a choice but, observing that the children were clearly not twins, my original question was now answered. How old was my friend?