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2015-09-04T12:34:29+08:00

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Find four consecutive even integers whose sum is 524.

Let first even integer: x
       second even integer: x + 2
       third consecutive even integer: X + 4
       fourth consecutive even integer: x + 6
       Sum= 524

Add:

(x) + (x+2) + (x+4) + (x+6) = 524
4x + 12 = 524
4x = 524 - 12
4x = 512

4x  =  512
 4         4
x =  128

The four consecutive integers are
first:  x = 128
second : x + 2 = 128 + 2 = 130
third:  x + 4 = 128 + 4 = 132
fourth: 128 + 6 = 134

FINAL ANSWER:  The four consecutive even integers are 128, 130, 132 and 134
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2015-09-04T13:28:11+08:00

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Cody is twice as old as Evan. Three years ago, the sum of their ages was 27. Find the age of each boy now.                
 
                                                                        
Representation: 
Let x = Evan's age     
                          2x = Cody's age         
                                                 
                                             Three years ago                      Now        
                   Cody                          2x - 3                                2x         
                   Evan                          x - 3                                   x          
                                      
Equation: (2x - 3) + (x - 3) = 27

Solution: (2x - 3) + (x - 3) = 27
               2x - 3 + x - 3 = 27
               3x - 6 = 27
               3x = 33
              -----   -----  ⇒ x = 11; 2x = 22
                3      3 

Answer: Cody is 22 while Evan is 11.

Check: (2x - 3) + (x - 3) = 27
            [2(11) - 3] + (11 - 3) = 27
            (22 - 3) + 8 = 27
            19 + 8 = 27
            27 = 27

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---Have a vigorous Friday---
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