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Question 530285: Hello, Could you please help me with this question in Algebra?
The product of two consecutive positive integers is 650. What are the two integers? Make sure to use quadratics to support your answer.
I thought of using X + X = 650 but not sure.
Thank you,
My e-mail address is Wicht@cox.net
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Two consecutive positive integers can be defined as 'x' and 'y', but then you have two unknowns.
So, the better way to define to consecutive integers is as 'x' and 'x+1'. Then it will go smoothly.
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x + (x+1) = 650 would be the sum, not the product.
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The product is defined by:
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x*(x+1) = 650
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Solving this...
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x^2 +x -650 = 0
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To factor, we need to find two multiplicands that a 1 apart and total 650.
A good place to start is the square root of 650.
Using the Google built-in calculator, just type 'sqrt(650)' in the Google search box to find:
sqrt(650) = 25.4950976
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Testing 25 and 26, we find their product is 650. Therefore, the quadratic can be factored as:
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(x+26)(x-25) = 0
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That means x = -26 or +25.
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We're looking for positive integers, so x=25 is chosen.
x+1 = 25 + 1 = 26
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Answer: Two consecutive positive integers whose product is 650 are 25 and 26.
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Done.
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