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 April 29th, 2012, 07:14 AM #1 Newbie   Joined: Feb 2012 Posts: 10 Thanks: 0 Difference of their ages Mary is younger than her husband, but their ages contain the same two digits. The sum of their ages is 11 times the difference of their ages. How old is Mary?
 April 29th, 2012, 08:17 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs Re: Difference of their ages Let M be Mary's age and H be the age of her husband. If $M_1$ is the tens digit and $M_2$ is the ones digit of Mary's age respectively, then we have: $M=10M_1+M_2$ $H=10M_2+M_1$ Using the given relationship between their ages, we have: $10M_1+M_2+10M_2+M_1=11$$10M_2+M_1-\(10M_1+M_2$$\)$ $11$$M_1+M_2$$=11$$9\(M_2-M_1$$\)$ $M_1+M_2=9$$M_2-M_1$$$ $4M_2=5M_1$ Hence: $M_1=4$ $M_2=5$ Mary is 45 years old.

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