In a cement factory, a machine takes one kilogram of cement. It then divides this into rectangles each weighing 10 g. These rectangles are then stamped into disks of cement each weighing 6 g with the remaining cement discarded. These cement disks are next packed into bags of 4 which are sealed and finally packed into boxes, each containing 6 bags ready for dispatch to the shops. What percentage weight of cement out of the original kilogram will be contained in COMPLETELY FILLED boxes (i.e. those containing a full 6 bags)?

Sure, let's break this down step by step:

1. First, we need to convert the kilogram of cement into grams because the weights of the rectangles and disks are given in grams. 1 kilogram = 1000 grams.

2. Next, we calculate how many rectangles can be made from 1000 grams. Since each rectangle weighs 10 grams, we divide 1000 by 10 to get 100 rectangles.

3. Each rectangle is then stamped into a disk weighing 6 grams. So, from 100 rectangles, we get 100 disks.

4. These disks are packed into bags of 4. So, we divide 100 by 4 to get 25 bags.

5. Finally, these bags are packed into boxes, each containing 6 bags. So, we divide 25 by 6. Since we are only interested in completely filled boxes, we ignore the remainder and get 4 boxes.

6. Now, we calculate the total weight of cement in the completely filled boxes. Each box contains 6 bags, each bag contains 4 disks, and each disk weighs 6 grams. So, the total weight is 4 boxes * 6 bags/box * 4 disks/bag * 6 grams/disk = 576 grams.

7. To find the percentage weight of the original kilogram that is contained in the completely filled boxes, we divide the weight of the cement in the boxes by the original weight and multiply by 100. So, (576 / 1000) * 100 = 57.6%.

Therefore, 57.6% of the original kilogram of cement will be contained in completely filled boxes.

Step 1: Convert the initial weight of cement from kilograms to grams. 1 kilogram = 1000 grams.

Step 2: Determine how many rectangles can be made from 1 kilogram of cement. Since each rectangle weighs 10 grams, you can make 1000/10 = 100 rectangles.

Step 3: Determine how much cement is used to make the disks. Since each disk weighs 6 grams, the total weight of cement used to make the disks from each rectangle is 6 grams. Therefore, the total weight of cement used to make the disks from all the rectangles is 100 rectangles * 6 grams/rectangle = 600 grams.

Step 4: Determine how many disks can be made from 1 kilogram of cement. Since each disk weighs 6 grams, you can make 600/6 = 100 disks.

Step 5: Determine how many bags can be filled with the disks. Since each bag contains 4 disks, you can fill 100 disks / 4 disks/bag = 25 bags.

Step 6: Determine how many boxes can be filled with the bags. Since each box contains 6 bags, you can fill 25 bags / 6 bags/box = 4 boxes (with 1 bag left over).

Step 7: Determine the total weight of cement in the completely filled boxes. Since each box contains 6 bags, and each bag contains 4 disks, and each disk weighs 6 grams, the total weight of cement in each box is 6 bags/box * 4 disks/bag * 6 grams/disk = 144 grams/box. Therefore, the total weight of cement in all the boxes is 4 boxes * 144 grams/box = 576 grams.

Step 8: Determine the percentage weight of cement in the completely filled boxes out of the original kilogram. Since 1 kilogram = 1000 grams, the percentage is (576 grams / 1000 grams) * 100% = 57.6%.