Several of my students (Left to right in photo: Danien Pineau-Valencienne, Ryan Conger, Tom Freeze, and Jonathan Barlow) mastered the quiz posted 23 Feb 2007 that follows:
Si Chang is the same age as her mother with the digits reversed. Last year her mother was 2.5 times as old as she was.
a. How old are Si and her mother?
b. Part a. can be done by trial and error, determmine the solution using algebra and logic.
The Solution (this one given by Indium's Bob Jarrett)
Si Chang and her Ma have ages with an interesting algebraic relationship. Let T be the tens digit in Si's age and U be the ones digit so Si is 10T+U currently. Ma is 10U+T. Last year Si was 10T+U-1 and M was 10U+T-1, which was 2.5 times Si's age.
This is a single equation with two unknowns:
2.5*(10T+U-1)=10U+T-1, defined by the line
This has an infinite number of solutions. However, only one solution exists with the additional constraints that the digits, U and T, must be integers from 0 to 9, inclusive.
Si is 13 and Ma is 31.