SOLUTION: Find three consecutive odd integers such that the product of the second and the third integers is twenty-six more than three times the first integer.

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Question 1181996: Find three consecutive odd integers such that the product of the second and the third integers is twenty-six more than three times the first integer.
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the middle number, so the three consecutive odd numbers are 

    (x-2),  x  and  (x+2),   in ascending order.


Then you write the equation as you read the problem

    x*(x+2) = 3*(x-2) + 26.


You simplify this quadratic equation

    x^2 + 2x = 3x - 6 + 26


and write it in the standard form'

    x^2 - x - 20 = 0.


Then you factor its left side

    (x-5)*(x+4) = 0,


and you see that it has the roots  x= 5  and x= -4.


-4 is not an odd number, so the only meaningful solution is  x= 5.


Thus the three numbers are  3,  5,  7.


It is the ANSWER, and you can CHECK it on your own, that the answer satisfies the problem's conditions.

Solved, answered and carefully explained.


Happy learning (!)