Associated Topics || Dr. Math Home || Search Dr. Math

### Borrowing and Returning Books

```
Date: 03/26/2001 at 17:16:57
From: Samantha Worthington
Subject: Working Backward

In her classroom, Mrs. Guelker has a shelf of books for students to
read. During the day, four students borrow books and eight students
return books. At the end of the day, there are 27 books on the shelf.
How many books were there at the beginning of the day?

I do not understand any of the problem, and need to figure out how you
```

```
Date: 03/27/2001 at 14:00:39
From: Doctor Ian
Subject: Re: Working Backward

Hi Samantha,

There is no way to solve the problem unless you assume that each
student borrows or returns exactly one book. If you assume that, then
you can solve the problem in the following way:

Let's use '?' to represent the number of books on the shelf at the
beginning of the day. Then after the four students borrow books, the
number of books on the shelf is:

? - 4

And after the eight students borrow books, the number of books on the
shelf is:

? - 4 + 8

We're told that this number is 27. So we know that:

? - 4 + 8 = 27

Can you find a number to substitute for '?' that will make this
equation true?

If you think of the equation as a balance beam,

? - 4 + 8         27
\_________/      \_____/
|_______________|
^

we can add to or remove anything from both sides without throwing it
out of balance, right? So we can add 4 to each side, which cancels out
the -4
on the left:

? + 8            27 + 4
\_________/      \______/
|_______________|
^

We can subtract 8 from each side, to cancel out the 8 on the left.

And that will leave us with '?' balancing some number - which will be
the number of books at the beginning of the day.

or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Puzzles
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search