An interesting application of algebra

     Owen Barfield wrote an unpublished novel English People.  On the official Owen Barfield website, chapters 1 - 8, 15-72, and 75 are available in pdf form.  Chapters 73 and 74 are published separately as The Rose on the Ash Heap and chapters 9 - 14 are missing.  They were loaned to an acquaintance of Barfield's who then lost them.  The website says that "the absence of these pages does not prevent the comprehension of the rest of the novel" and these chapters comprised about 6% of the novel.  So, one might wonder, about how many pages is that?

    This is one of the few times in my life that I have actually used algebra to find out something I wanted to know and it came up completely unexpectedly.  But it is exactly what we need here.  

    The official Owen Barfield website gives the number of pages of each of the pdfs: 

Chapters 1 - 8: 61 pages 

Chapters 15 - 24: 47 pages 

Chapters 25 - 32: 34 pages 

Chapters 34 - 42: 50 pages 

Chapters 43 - 51: 62 pages 

     Chapters 52 - 62: 47 pages 

Chapters 63 - 75 (except 73 and 74): 42 pages  

    Altogether, we have 343 pages collected into pdfs.  The chapters published as The Rose on the Ash Heap comprise 10% of the novel.  So, in total, we are missing 16%.  The website also says that the original manuscript is 550 pages long.  But since this manuscript is currently held in the Bodleian library, it must not contain the missing chapters.  Also, the 550 may refer to handwritten pages and we are dealing with pdfs, so we do not really know how long the original was.  But we can figure it out.  I believe the 10% for Rose on the Ash Heap refers to 10% of the original novel.  

    So, 343 pages is 84% of the original length of the novel.  Let X be the number of pages in the original novel.  Then, 0.84X = 343.  Hence, 343/0.84 = X.  Therefore, the original novel would have been about 408 pdf pages.  10% of 408 is about 41 pages.  6% of 408 is around 24 pages.  So, the novel that has been preserved is only missing 24 pages.  

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