It will cost Luigi approximately $514.55 to shelve the books and DVDs.
How do we calculate the cost?
We shall determine the total cost of shelving Luigi's books and DVDs in the is way:
Given:
Lengths for the DVDs = 7.5, 5.3, and 0.6 inches.
Lengths for the Books = 9.5, 5.4, and 1 1/3 (or 3.7) inches.
Length for 1 shelf = 30.5 inches
Cost of 1 shelf = $12.55
No. of books = 42
No. of DVD = 35
First, we find the total length of each of the items:
For books:
Total length of books = 42 books * (9.5 + 5.4 + 1 1/3)
= 42 * 18.6
≈ 781.2 inches
For DVDs:
Total length of DVDs = 35 DVDs * (7.5 + 5.3 + 0.6)
= 35 * (13.4 inches)
= 469 inches
Total length of books and DVDs = 781.2 inches + 469 inches
≈ 1250.2inches
Next, we shall find the total number of shelves Luigi needs:
Number of shelves = Total length / Length of each shelf
= 1250.20 inches / 30.5 inches (length of each shelf)
= 40.99 shelves
We can round to the nearest whole number since Luigi cannot buy a fraction of a shelf, which is = 41 shelves.
Then, we estimate the cost:
Total cost = Number of shelves * Cost per shelf
= 41 shelves * $12.55 per shelf
≈ $514.55
So, it will cost Luigi ≈ $514.55 to shelve the books and DVDs.