SOLUTION: a bookcase has 5 shelves. Each shelf is 2 3/4 feet wide. A set of 35 reference books will be placed on the shelves. As many reference books as possible will be placed on each shelf

Question 726596: a bookcase has 5 shelves. Each shelf is 2 3/4 feet wide. A set of 35 reference books will be placed on the shelves. As many reference books as possible will be placed on each shelf. Each reference book is 1/4 foot wide. How many shelves will be used for the reference books? show your work.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would call this problem a 2-step arithmetic word problem.
It requires:
knowing how to handle fractions and
not having been taught that math is difficult and must be feared.

STEP 1 - How many books fit on 1 shelf?
We divide feet by feet.
We could use fractions, or decimals.
We could even transform both measurements to inches.
The result is that feet divided by is 11 exactly.
It divides evenly, so we can fit 11 books per shelf, tightly packed, with no room to spare.
Calculation using fractions:
(transforming mixed number into improper fraction)
��
Calculation using decimals:
If we know that
and we know that
and we can use a calculator, it is to divide

If we prefer to measure in inches we would think that
the shelf width is 33 inches
and each book is 3 inches wide,
so we divide to find that 11 books fit on each shelf.

STEP 2 -How many shelves will be used?
We divide the 35 books into piles of 11 books.
We find that we can make 3 piles of 11 books, and we will have 2 books left over.
We will need shelves (and a bookend).
Three (3) shelves could have 11 books (full shelves),
but you need at least one more shelf, for a total of 4 shelves.
If the first 3 shelves are filled with 11 books each,
the fourth shelf could hold the remaining 2 books.
Or you could arrange the books differently, but you need at least 4 shelves.
The calculation:
1 pile = 1 x 11 books = 11 books
2 piles = 2 x 11 books = 22 books
3 piles = 3 x 11 books = 33 books
4 piles = 4 x 11 books = 44 books
Obviously, we can make 3 piles of 11 books, and we will have 2 books left over.
35 - 33 = 2
The teacher would say that 35 divided by 11 is 3 with a remainder of 2.
When we do long division, we do exactly the calculations above.

THE WRONG WAY:
Someone could figure that 35 books at foot per book require
feet of shelf space.
Then, dividing the space needed by the space per shelf,
35/4 feet divided by feet,
that person could find that 3&2/11 shelves are needed,
and round up to 4 shelves.
The result is the same in this case, but the approach is wrong,
because if the measures of book and shelf width were different,
you might find a number of shelves that could not hold the books,
unless we cut some of the books in pieces.

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