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2015-09-03T10:55:38+08:00

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Ten years ago:
  Son = x
  Mother = 5x

Present:
  Son:  x + 10
  Mother:  5x + 10
  Sum of their ages today: 55

Equation:
 (x+10) + (5x + 10) = 55
  x + 5x + 10 + 10 = 55
  6x + 20 = 55
  6x = 55 - 20
  
 6x = 35
  6       6

x = 35/6

Substitute:
Present Age:
  Son:  x + 10  
            = 35/6 + 10
            = 35/6 + 60/6
            = 95/6 , or 15 and 5/6 years ,  or 15 years and 10 months 

Mother's age:  5x + 10
                       = 5 (35/6) + 10
                       = 175/6 + 60/6
                       = 235/6 , or  39 and 1/6 years,   or  39 years and 2 months

FINAL ANSWER, AGES TODAY:
   SON'S AGE:  15 and 5/6 years (15 years and 10 months)
   MOTHER'S AGE :   39 and 1/6 years (39 years and 2 months)

To check the sum of their ages today:
  (x + 10) + (5x + 10) = 55
  (35/6  + 10)  +  (5×35/6  + 10) = 55
   (35/6 + 60/6) + (175/6 + 60/6) = 55
    95/6   +   235/6 = 55
               330/6  = 55
               330÷6 = 55
                     55 = 55
                        

           


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