# direct an inverse variation

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The number of books checked out from the library varies directly with the number of book reports assigned. There were 3375 books checked out when there were 225 book reports assigned.

How many book reports have been assigned if there are 13,500 books

• direct an inverse variation -

Since the number of books checked out varies directly with the number of book reports assigned we have the following relationship:
Let B be the number of books checked out and R be the number of reports due.
Then because R and B vary directly there is a constant K so that
B = K*R
If you prefer we could also use a different constant C and write
C*B = R.
For this particular problem,
3375 = K* 225
We can solve for K as
K= 3375/225 = 15.

So if the number of Reports R when there are 13500 books checked out is given by
13500=15*R
So R=13500/15=900. And this is our answer.

Another way to look at the problem is to recognize that for direct variation the ratio of the two quantities is a constant, so that we could set up the proportion:
225/3375 = R/13500
Cross multiplying gives
225*13500=3375*R
solving for R by dividing both sides by 3375 gives us
225*13500/3375 = 900 = R

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