(O-O)

There are some books on three shelves. On the bottom shelf there are half as many books as on the other two shelves. On the middle shelf there are three times less than on the other two shelves. On the top shelf there are 30 books. How many books are on all three shelves?

60 books

Step-by-step explanation:

Let x stand for the number of books on the bottom bookshelf now (the answer to the question). This is 15 more than were there to begin with.

The number on the top shelf now is 2x, which is 15 less than were there to begin with. So, you can write the relation ...

 2x +15 = 3(x -15) . . . . there were 3 times as many books on the top shelf to begin with

 2x + 15 = 3x -45 . . . . eliminate parentheses

 60 = x . . . . . . . . . . . . add 45-2x

The number of books in the bottom bookshelf now is 60.

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