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2015-04-06T13:58:38+08:00

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Sarah is four years younger than Joe. In five years, Joe will be twice Sarah's age now. How old are they now?
(SOLUTION 1)

Representation: Let x = Joe's age
                        x - 4 = Sarah's age
                      
                                       Present                   In five years
                 Sarah                x - 4                    x - 4 + 5 =  x + 1
                 
                 Joe                     x                            x + 5

Equation: In five years, Joe will be twice Sarah's age now, so, our equation would be: x + 5 = 2(x - 4)

Solution: x + 5 = 2(x - 4)
              x + 5 = 2x - 8
              Isolate the variable -- which means, group the variables on a certain side.
              x - 2x = -8 - 5
              - x = -13
             ---------------
              - x = -x
              x = 13; x - 4 = 9
Answer: Joe is  13 years old while Sarah is 9 years old.
      
Check: x + 5 = 2(x - 4)
           13 + 5 = 2(13 - 4)
           18 = 26 - 8
           18 = 18
      
(SOLUTION 2)


Representation: Let x = Sarah's age
                        x + 4 = Joe's age
 
                                      Present                   In five years
                 Sarah                x                              x + 5
                 
                  Joe                x + 4                    x + 4 + 5 = x + 9

Equation: In five years, Joe will be twice Sarah's age now, so, the equation would be: x + 9 = 2x

Solution: x + 9 = 2x
              9 = 2x - x
              9 = x
              x = 9; x + 4 = 13

A
nswer: Sarah is 9 years old while Joe is 13 years old.

Check: x + 9 = 2x
           9 + 9 = 2(9)
           18 = 18
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