A box contains 90 screws, each weighing 100 grams, and 100 bolts, each weighing 150 grams. The total weight of the box plus its contents is 35.5 kilograms. What is the weight of the empty box (in kilograms)?

Introduction / Context:
This is a straightforward arithmetic and unit conversion problem that tests understanding of mass, addition, and subtraction. We are given the total weight of a box and its contents, as well as the individual weight and count of screws and bolts inside. The goal is to find the weight of the empty box itself by subtracting the weight of all the items from the total weight.

Given Data / Assumptions:

• Number of screws = 90.
• Weight of each screw = 100 grams.
• Number of bolts = 100.
• Weight of each bolt = 150 grams.
• Total weight of box plus contents = 35.5 kilograms.
• 1 kilogram = 1000 grams.

Concept / Approach:
The total weight of the contents equals the sum of the weight of all screws and the weight of all bolts. Once we find this in kilograms, we subtract it from the total weight (box plus contents) to get the weight of the empty box. Unit conversion is required because the item weights are given in grams while the total is in kilograms. Converting everything to kilograms avoids confusion and keeps calculations consistent.

Step-by-Step Solution:
Step 1: Compute total weight of screws. Each screw weighs 100 grams, and there are 90 screws.Step 2: Total screw weight = 90 * 100 grams = 9000 grams.Step 3: Convert 9000 grams to kilograms: 9000 / 1000 = 9 kilograms.Step 4: Compute total weight of bolts. Each bolt weighs 150 grams, and there are 100 bolts.Step 5: Total bolt weight = 100 * 150 grams = 15000 grams.Step 6: Convert 15000 grams to kilograms: 15000 / 1000 = 15 kilograms.Step 7: Total weight of contents = 9 kilograms + 15 kilograms = 24 kilograms.Step 8: Total weight of box plus contents = 35.5 kilograms.Step 9: Weight of empty box = 35.5 kilograms - 24 kilograms = 11.5 kilograms.

Verification / Alternative check:
You can convert the final answer back to grams to double check. Weight of empty box = 11.5 kilograms = 11500 grams. Adding back the contents: 11500 grams (box) + 9000 grams (screws) + 15000 grams (bolts) = 35500 grams. Converting 35500 grams to kilograms gives 35500 / 1000 = 35.5 kilograms, which matches the given total weight. This confirms that the calculation is consistent.

Why Other Options Are Wrong:
Option 10.5 kgs: This would imply contents weigh 25 kilograms, which does not match the given numbers.Option 12 kgs: Would lead to total contents weight of 23.5 kilograms, contradicting the actual content weights.Option 9.6 kgs: Comes from an incorrect combination or unit conversion error.Option 8.5 kgs: Underestimates the box weight significantly and does not satisfy the total of 35.5 kilograms.

Common Pitfalls:
Students may forget to convert grams to kilograms, leading to incorrect subtraction. Another frequent mistake is miscalculating the total number of grams by mixing up the counts or weights of screws and bolts. Carefully separating each part of the calculation and checking the arithmetic at every step helps avoid these errors.

Final Answer:
The weight of the empty box is 11.5 kgs.