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Charles and James are both math professors. One day Charles and James have the following conversation:...

Charles and James are both math professors. One day Charles and James have the following conversation:

Charles: How many kids do you have?

James: I have 3 kids. Charles: How old are your kids?

James: If x, y, and z are the ages of my kids and d is my office number, then x*z*y= 36 and x+y+z=d .

Charles: I know your office number, and you have not given me enough information to figure out the ages of your kids.

James: My oldest just came down with a cold.

Charles: I now know the ages of your kids!

What are the ages of James’s kids? Justify your answer. For this problem you may assume that the ages of James’s kids are all positive integers and that James’s office number is an integer.

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