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#