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A bookshelf is 42 inches long.

a. How many books of length [tex]1 \frac{1}{2}[/tex] inches will fit on the bookshelf? Explain your reasoning.

b. A bookcase has 5 of these bookshelves. How many feet of shelf space is there? Explain your reasoning.

Answer :

Sure! Let's solve the problem step-by-step.

### Part a:

To figure out how many books that are [tex]\(1\frac{1}{2}\)[/tex] inches long will fit on a 42-inch bookshelf, we need to divide the total length of the shelf by the length of each book.

1. Convert the mixed fraction to a decimal:
[tex]\[
1\frac{1}{2} = 1.5 \text{ inches}
\][/tex]

2. Determine how many 1.5-inch books can fit:
Divide the total length of the bookshelf by the length of one book.
[tex]\[
42 \div 1.5 = 28
\][/tex]

So, you can fit 28 books, each [tex]\(1\frac{1}{2}\)[/tex] inches long, on the 42-inch bookshelf.

### Part b:

Now we calculate the total shelf space for a bookcase with 5 shelves.

1. Convert the length of one bookshelf from inches to feet:
[tex]\[
42 \text{ inches} = \frac{42}{12} = 3.5 \text{ feet}
\][/tex]
(Note: There are 12 inches in a foot.)

2. Calculate the total shelf space in feet:
Multiply the length of one shelf (in feet) by the number of shelves.
[tex]\[
3.5 \text{ feet per shelf} \times 5 \text{ shelves} = 17.5 \text{ feet}
\][/tex]

The total shelf space is 17.5 feet for the bookcase with 5 shelves.

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