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The Young Girl's Age (Posted on 2017-12-25) Difficulty: 3 of 5
The following facts are known about the ages of A, B & C:
- You can get A's age by transposing the two digits of B's age.
- B is 10 times as old as C.
- Twice C's age equals the difference between the ages of A and B.

How old is the youngest?

No Solution Yet Submitted by Ady TZIDON    
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algebraic solution Comment 2 of 2 |
Let B=10x+y with x and y integers.

Then the problem conditions can be expressed in terms of x and y.

A=10y+x
C=x+y/10
2(x+y/10)=9y-9x

From the last equation, x=(4/5)y.  Integral x requires y=5 so x=4.

Then the ages are A=54, B=45, C=4.5.

  Posted by xdog on 2017-12-26 09:08:31
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