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Answer :
Let's break down the problem step by step:
### Part a:
We need to find out how many books, each with a length of [tex]\(1 \frac{1}{2}\)[/tex] inches, can fit on a 42-inch long bookshelf.
1. Convert the mixed number to an improper fraction or decimal:
[tex]\(1 \frac{1}{2}\)[/tex] inches can be converted to 1.5 inches.
2. Divide the total length of the bookshelf by the length of one book:
[tex]\[
\frac{42}{1.5} = 28
\][/tex]
This means that 28 books, each measuring 1.5 inches, can fit on the bookshelf.
### Part b:
Now, we need to calculate the total amount of shelf space in feet for a bookcase that has 5 of these 42-inch bookshelves.
1. Convert the length of each bookshelf from inches to feet:
Since there are 12 inches in a foot, we convert 42 inches to feet:
[tex]\[
\frac{42}{12} = 3.5 \text{ feet per bookshelf}
\][/tex]
2. Multiply the length in feet by the number of bookshelves (5):
[tex]\[
3.5 \times 5 = 17.5 \text{ feet}
\][/tex]
Therefore, the total shelf space for 5 such bookshelves is 17.5 feet.
By following these steps, we determined that 28 books fit on one shelf, and the total shelf space for 5 shelves is 17.5 feet.
### Part a:
We need to find out how many books, each with a length of [tex]\(1 \frac{1}{2}\)[/tex] inches, can fit on a 42-inch long bookshelf.
1. Convert the mixed number to an improper fraction or decimal:
[tex]\(1 \frac{1}{2}\)[/tex] inches can be converted to 1.5 inches.
2. Divide the total length of the bookshelf by the length of one book:
[tex]\[
\frac{42}{1.5} = 28
\][/tex]
This means that 28 books, each measuring 1.5 inches, can fit on the bookshelf.
### Part b:
Now, we need to calculate the total amount of shelf space in feet for a bookcase that has 5 of these 42-inch bookshelves.
1. Convert the length of each bookshelf from inches to feet:
Since there are 12 inches in a foot, we convert 42 inches to feet:
[tex]\[
\frac{42}{12} = 3.5 \text{ feet per bookshelf}
\][/tex]
2. Multiply the length in feet by the number of bookshelves (5):
[tex]\[
3.5 \times 5 = 17.5 \text{ feet}
\][/tex]
Therefore, the total shelf space for 5 such bookshelves is 17.5 feet.
By following these steps, we determined that 28 books fit on one shelf, and the total shelf space for 5 shelves is 17.5 feet.
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