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Problem Solving/Word Problem
Jame's Dad is 5 times older than James and James is twice as old as his sister Sara. In two years, the sum of their ages will be 58. How old is James now?


Sagot :

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James' Dad is 5 times older than James and James is twice as old as his sister Sara. In two years, the sum of their ages will be 58. How old is James now? 

Representation: Let x = Sara's age
                         2x = James' age
                        10x = Their dad's age
  
                                           Now                             In two years
                  Sara                   x                                     x + 2
                James                 2x                                   2x + 2
                  Dad                  10x                                 10x + 2

Equation: (x + 2) + (2x + 2) + (10x + 2) = 58

Solution: (x + 2) + (2x + 2) + (10x + 2) = 58
                x + 2 + 2x + 2 + 10x + 2 = 58
               13x + 6 = 58
               13x = 52
               -----   -----  ⇒  x = 4; 2x = 8; 10x = 40
                13    13
                  
Answer: James is 8 years old.

Check: (x + 2) + (2x + 2) + (10x + 2) = 58
            (4 + 2) + [2(4) + 2) + [10(4) + 2) = 58
            6 + (8 + 2) + (40 + 2) = 58
            6 + 10 + 42 = 58
            58 = 58

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