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2016-02-09T18:03:40+08:00

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Sum of present ages:
     x + y = 45
           y = 45 - x

Present ages:
   Robin: x
   Bruno: 45 - x

Ages seven years ago:
   Robin:  x - 7
   Bruno: 45 - 7 - x  or   38 - x

Equation:
  
   x - 7 = 16 + ¹/₂ (38 - x) 
   
   x - 7 = 16 + 19 - x/2 
 
   x - 7 = 35 - x/2
  
   (2) (x-7) = (35-x/2) (2)

    2x - 14 = 70 - x
   
    2x + x = 70 + 14
   
    3x = 84

    3x/3 = 84/3
   
    x = 28

Present ages:  Plug-in 28 to x
   Robin:  28 years old
   Bruno:  45 - 28 = 17 years old

Ages seven years ago:
   Robin: 28 - 7 = 21 years old
   Bruno: 17 - 7 = 10 years old

ANSWER:  Bruno was 10 years old (seven years ago).

Check
Sum of their ages at present is 45.
   28 + 17 = 45
   45 = 45   (True)

Comparison of ages seven years ago:
   21 = ¹/₂ (10) + 16
   21 = 5 + 16
   21 = 21   (True)
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