SOLUTION: Hello, Could you please help me with this problem about integers? I have no clue on how to find them, I dont know the formula or how to solve this word problem equation...any help

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Hello, Could you please help me with this problem about integers? I have no clue on how to find them, I dont know the formula or how to solve this word problem equation...any help      Log On


   

Question 134130: Hello,
Could you please help me with this problem about integers? I have no clue on how to find them, I dont know the formula or how to solve this word problem equation...any help would be appreciated.
The product of two consecutive odd integers is 1 less than 3 times their sum. Find the integers.

Thank you so much,
Mrs. Gibson
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The odd integers are spaced every 2 numbers
1%2C3%2C5%2C7%2C9. . .etc.
Call the smallest odd integer n
The next odd integer will be n+%2B+2
The product of these integers is n%2A%28n+%2B+2%29
Three times their sum is 3%2A%28n+%2B+%28n+%2B2%29%29
n%2A%28n%2B2%29+=+3%2A%28n+%2B+%28n+%2B+2%29%29+-+1
n%5E2+%2B+2n+=+3%2A%282n+%2B+2%29+-+1
n%5E2+%2B+2n+=+6n+%2B+6+-+1
n%5E2+-+4n+-+5+=+0
%28n+-+5%29%28n+%2B+1%29+=+0
n+=+5
n+=+-1 This choice is not what is wanted
If n+=+5, then
n+%2B+2+=+7
The integers are 5 and 7
check answer
n%2A%28n%2B2%29+=+3%2A%28n+%2B+%28n+%2B+2%29%29+-+1
5%2A%285%2B2%29+=+3%2A%285+%2B+%285+%2B+2%29%29+-+1
35+=+3%2A%2812%29+-+1
35+=+36+-+1
35+=+35
OK