You installed a bookshelf on the wall to organize some of your books. The books that you absolutely want on the shelf weigh a total 6 3/4 pounds. The bookshelf can handle no more than 9 pounds. You plan on filling the rest of the shelf with your paperbacks that each weigh about 1/8 pound. Assuming you won't run out of room,how many paperback books can you add to the shelf

Question

You installed a bookshelf on the wall to organize some of your books. The books that you absolutely want on the shelf weigh a total 6 3/4 pounds. The bookshelf can handle no more than 9 pounds. You plan on filling the rest of the shelf with your paperbacks that each weigh about 1/8 pound. Assuming you won't run out of room,how many paperback books can you add to the shelf

Answer 1

(9 - 6.75) / 0.125 = ?

Answer 2

To determine the number of paperback books you can add to the shelf, you need to find the weight capacity remaining after placing the books you want on the shelf.

First, let's convert the weight of the books you want on the shelf to a common denominator.

6 3/4 pounds = (4 * 6) + 3 = 27/4 pounds

Next, subtract the weight of the books you want on the shelf from the maximum weight capacity of the shelf:

9 pounds - 27/4 pounds = (36/4) pounds - (27/4) pounds = 9/4 pounds

Now, divide the remaining weight capacity by the weight of each paperback book:

(9/4 pounds) / (1/8 pound) = (9/4 pounds) * (8/1 pound) = 72/4 pounds = 18 paperback books

Therefore, you can add 18 paperback books to the shelf.

Answer 3

To find out how many paperback books you can add to the shelf, you need to determine how much weight capacity is left after placing the books you absolutely want on the shelf.

First, convert the mixed number 6 3/4 pounds to an improper fraction.

6 3/4 = (6 * 4 + 3)/4 = 27/4 pounds

Next, subtract the weight of the books you absolutely want from the maximum weight capacity of the bookshelf.

9 pounds - 27/4 pounds = (9 * 4/1 - 27/4) pounds
= (36/1 - 27/4) pounds
= (36 * 4/4 - 27/4) pounds
= (144/4 - 27/4) pounds
= (117/4) pounds

Now, you have the weight capacity left on the shelf, which is 117/4 pounds.

Since each paperback book weighs 1/8 pound, you can calculate how many books you can add by dividing the weight capacity left by the weight of each book.

117/4 pounds ÷ 1/8 pound/book = (117/4) ÷ (1/8)
= (117/4) × (8/1)
= (117 × 8) ÷ (4 × 1)
= 936/4
= 234

Therefore, you can add 234 paperback books to the shelf without exceeding the weight capacity.