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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.
### 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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