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 Question from Johanna: Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third

Hi Johanna,

Every odd integer is 1 more than an even integer and every even integer is a multiple of 2, hence every odd integer can be written $2n + 1$ for some integer $n.$ I am going to write the middle of the three consecutive integers as $2n + 1.$ The next odd integer is 2 more than $2n + 1$ so it is $2n + 1 + 2 = 2n+3.$ The odd integer previous to $2n + 1$ is 2 less than it so it is $2n + 1 - 2 = 2n - 1.$

Now you have your three consecutive odd integers, $2n-1, 2n+1$ and $2n+3.$ Use the fact that "the sum of the first and second is 31 less than 3 times the third" to write an equation and solve for $n.$