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Mathematics

OpenStudy (anonymous):
Sonja has 1/6 fiction books, 1/3 nature books, and 12 mystery books. How many books does she have in all?

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OpenStudy (sandra):
hmmm, there is some missing information here I think

OpenStudy (anonymous):
That is what I thought too...I was trying to help my cousin, but that is all the information that was on their worksheet.

OpenStudy (sandra):
well, maybe not.

OpenStudy (sandra):
ok so let's set this up

OpenStudy (sandra):
if the total number of books is X, then we know that 1/6x are fiction, 1/3x are nature, and 12 are mystery

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OpenStudy (sandra):
so 1/6x + 1/3x + 12 = X

OpenStudy (sandra):
so 12 = x - 1/6x - 1/3x
or 12 = 1/2x
so x = 12/.5 = 24

OpenStudy (sandra):
so the total number of books is 24, and precisely 12 mystery, 4 fiction and 8 nature

OpenStudy (anonymous):
Thanks!!

OpenStudy (sandra):
no problem! the key assumption is that , that's all the types of books there are

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OpenStudy (sandra):
the reason it works is they basically tell you that half the books are mystery , since if 1 - 1/3 - 1/6 = 1/2

OpenStudy (sandra):
good luck!

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