Question 191706: The sum of three numbers is 27 and their product is 585. Find the numbers.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The sum of three numbers is 27 and their product is 585. Find the numbers.
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It's 3 unknowns and only 2 equations, not straightforward math.
Factor 585
585 = 3 x 3 x 5 x 13
13 has to be one of the numbers, because if it's multiplied by 3 or 5 the 27 is exceeded.
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Now it's 2 numbers that add to 14 and the product is 45.
We can use algebra, but it's obvious they're 5 and 9.
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x + y = 14 --> x = 14-y
x*y = 45
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sub for x
(14-y)*y = 45
y^2 - 14y + 45 = 0
(y-5)*(y-9) = 0
y = 5
y = 9
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5, 9 and 13
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