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December 21, 2014

December 21, 2014

Posted by **Anonymous** on Wednesday, October 10, 2012 at 2:08pm.

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

- direct an inverse variation -
**Ed**, Wednesday, October 10, 2012 at 2:24pmSince 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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