SOLUTION: The product of two consecutive odd integers is 22 more than 7 times the larger number. Use a quadratic equation to determine the two integers. I was thinking it would look some

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Question 828432: The product of two consecutive odd integers is 22 more than 7 times the larger number. Use a quadratic equation to determine the two integers.
I was thinking it would look something like:
x(2+x) = 22 + 7(2+x)
x (2 +x) - 7(2+x)-22 = 0
x^2 + 9 - 36
which you would then factor to get the two numbers. The answer is 9 and 11. I am not sure how you get this answer. Thank you for your help!
Found 2 solutions by Seutip, MathTherapy:
Answer by Seutip(231) About Me  (Show Source):
You can put this solution on YOUR website!
The product of two consecutive odd integers is 22 more than 7 times the larger number. Use a quadratic equation to determine the two integers.
And no need to worry you are indeed correct. :)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The product of two consecutive odd integers is 22 more than 7 times the larger number. Use a quadratic equation to determine the two integers.
I was thinking it would look something like:
x(2+x) = 22 + 7(2+x)
x (2 +x) - 7(2+x)-22 = 0
x^2 + 9 - 36
which you would then factor to get the two numbers. The answer is 9 and 11. I am not sure how you get this answer. Thank you for your help!


You're correct up to here: x(2 + x) - 7(2 + x) - 22 = 0

2x+%2B+x%5E2+-+14+-+7x+-+22+=+0 ----- Distributing

x%5E2+%2B+2x+-+7x+-+14+-+22+=+0 ----- COLLECTING like-terms

x%5E2+-+5x+-+36+=+0 ------ COMBINING like-terms



Solving this quadratic equation should result in x either being highlight%289_or_-+4%29



Note that x CANNOT be - 4, since the problem states that the integers are odd, and - 4 is NOT ODD. Therefore,

the solution, x = - 4 is ignored.



Since x, in this case is the smaller integer, and is 9, then other odd integer = 9 + 2, or 11. 



Odd integers: highlight_green%289_and_11%29

You can do the check!! 



If you need a complete and detailed solution, let me know!!



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 

	

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