The product of two consecutive odd integers is 22 less than 15 times the smaller integer. What are the integers?

1 Answer
Jun 20, 2016

The two integers are 11 and 13.

Explanation:

If x represents the smaller integer, the larger integer is x+2, as the integers are consecutive and 2+ an odd integer will give the next odd integer.

Converting the relationship described in words in the question into a mathematical form gives:
(x)(x+2) = 15x - 22

Solve for x to find the smaller integer
x^2 + 2x = 15x - 22 \text{ Expand left hand side}
x^2 -13x + 22 = 0 \text{ Rearrange into quadratic form}
(x-11)(x-2) = 0 \text{ Solve quadratic equation}

The quadratic equation is solved for
x = 11 or x = 2

As the question specifies the integers be odd, x=11 is the only useful solution.

The smaller integer is x = 11
The larger integer is x+2 = 13