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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