SOLUTION: April, Mae, june and Julie were born in consecutive years, in that order, with april being the oldest. All they will tell you is that the sum of the squares of their ages is 534. H

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Question 131572: April, Mae, june and Julie were born in consecutive years, in that order, with april being the oldest. All they will tell you is that the sum of the squares of their ages is 534. How old are they?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
April, Mae, June and Julie were born in consecutive years, in that order, with april being the oldest. All they will tell you is that the sum of the squares of their ages is 534. How old are they?


 Let Julie's age = X
 then June's age = X+1
   and Mae's age = X+2
 and April's age = X+3

                   X² + (X + 1)² + (X + 2)² + (X + 3)² = 534

X² +  (X + 1)(X + 1) + (X + 2)(X + 2) + (X + 3)(X + 3) = 534

    X² + (X² + 2X + 1) + (X² + 4X + 4) + (X² + 6X + 9) = 534  

          X² + X² + 2X + 1 + X² + 4X + 4 + X² + 6X + 9 = 534

                                        4X² + 12X + 14 = 534

                                       4X² + 12X - 520 = 0  

Divide every term by 4
 
                                         X² + 3X - 130 = 0

                                      (X + 13)(X - 10) = 0

                                      Solutions are -13 and 10.
                                      
Discard the negative answer.  So 

X = 10 = Julie's age, so
Julie's age = X = 10
June's age = X+1 = 10+1 = 11
Mae's age = X+2 = 10+2 = 12
April's age = X+3 = 10+3 = 13

Edwin
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