One shelf at Cover-to-Cover Bookstore contains copies of several books on the best-seller list. Half of the books on the shelf are copies of the Number 1 best- seller. Of the remainder, 1/4 are copies of the Number 3 book. The rest are copies of the Number 2 book. If there are 5 copies the Number 2 book, how many best sellers are on the shelf?
You are welcome.
To find the number of best-sellers on the shelf, let's break down the information given in the question.
We know that half of the books on the shelf are copies of the Number 1 best-seller. So, if we let "x" represent the total number of best-sellers on the shelf, we can say that x/2 represents the number of copies of the Number 1 best-seller.
We are also given that 1/4 of the remaining books (after excluding the Number 1 best-seller) are copies of the Number 3 book. This means that 3/4 of the remaining books are copies of the Number 2 book.
Now, if we deduct the copies of the Number 1 and Number 3 books from the total number of books on the shelf, we get the number of copies of the Number 2 book, which is 5.
So, we can set up the equation:
x/2 + x/4 + 5 = x
To solve this equation, we'll first combine the like terms:
2x/4 + x/4 + 5 = x
Now, we'll find a common denominator for 2x/4 and x/4:
(2x + x)/4 + 5 = x
Simplifying further:
3x/4 + 5 = x
To eliminate the fraction, we'll multiply the entire equation by 4:
4 * (3x/4 + 5) = 4 * x
3x + 20 = 4x
Next, we'll subtract 3x from both sides:
3x + 20 - 3x = 4x - 3x
20 = x
Therefore, there are 20 best-sellers on the shelf.
THANKS A MILLION!
n on shelf
.5 n are #1
.25 * .5 n = .125 n are #3
.5 n + .125 n = .625 n are either #1 or #3
so
1 n-.625 n = .375 n = 5
n = 5/.375 = 13 1/3
hmmmm, I hope we have a fractional bookcase