The page numbers of an open book totalled $871$. At what pages was the book open?

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So far I have $x + (x-1) = 871$. This has led to one page being $435$ and the other, $436$. Is there anything needing alteration, or is this equation workable?

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This equation (the equation you wrote) works. x+ (x−1) = 871. However, the equation x + (x + 1) = 871 also works, since these two numbers are also consecutive numbers.

Edit: The solution to the second equation yields the exact same answer.

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The layout of the book does not matter. As long as the numbers add up to $871$, then the answer is correct.