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

The two integers are

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The two consecutive odd integers are 7 and 9.

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Let ( x ) represent the smaller odd integer. Then the next consecutive odd integer would be ( x + 2 ). According to the given conditions:

[ x(x + 2) = 15x - 22 ]

Expanding and rearranging terms:

[ x^2 + 2x = 15x - 22 ] [ x^2 - 13x + 22 = 0 ]

Factoring or using the quadratic formula:

[ (x - 11)(x - 2) = 0 ]

The solutions for ( x ) are ( x = 11 ) or ( x = 2 ). However, since we're considering odd integers, the correct solution is ( x = 11 ). Therefore, the smaller integer is 11 and the next consecutive odd integer is ( 11 + 2 = 13 ). So, the integers are 11 and 13.

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