Solving Weight Relationships for Objects K, L, M, N, O

This question asks us to find the weight of object N based on a series of relationships between the weights of five objects: K, L, M, N, and O. We are given specific weights and relative weights and need to work through the information provided to find the unknown weight.

Given Information about Object Weights

• The weight of M is 60 kg.
• L is twice as heavy as N, which can be written as \(L = 2 \times N\).
• O weighs thrice as heavy as L, which can be written as \(O = 3 \times L\).
• K weighs half the weight of O, which can be written as \(K = \frac{1}{2} \times O\) or \(K = 0.5 \times O\).
• K weighs equal to M, which means \(K = M\).

Step-by-Step Calculation to Find the Weight of N

We can use the given information to find the weights of the objects step by step, eventually leading to the weight of N.

Step 1: Find the weight of K.

We are given that the weight of M is 60 kg, and K weighs equal to M. So, the weight of K is also 60 kg.

\[K = M = 60 \text{ kg}\]

Step 2: Find the weight of O.

We know that K weighs half the weight of O (\(K = 0.5 \times O\)). We just found that K weighs 60 kg. We can use this to find the weight of O.

\[60 \text{ kg} = 0.5 \times O\]

To find O, we can divide the weight of K by 0.5 (or multiply by 2):

\[O = \frac{60 \text{ kg}}{0.5} = 60 \text{ kg} \times 2 = 120 \text{ kg}\]

So, the weight of O is 120 kg.

Step 3: Find the weight of L.

We are given that O weighs thrice as heavy as L (\(O = 3 \times L\)). We found that O weighs 120 kg. We can use this to find the weight of L.

\[120 \text{ kg} = 3 \times L\]

To find L, we can divide the weight of O by 3:

\[L = \frac{120 \text{ kg}}{3} = 40 \text{ kg}\]

So, the weight of L is 40 kg.

Step 4: Find the weight of N.

Finally, we are given that L is twice as heavy as N (\(L = 2 \times N\)). We found that L weighs 40 kg. We can use this to find the weight of N.

\[40 \text{ kg} = 2 \times N\]

To find N, we can divide the weight of L by 2:

\[N = \frac{40 \text{ kg}}{2} = 20 \text{ kg}\]

Thus, the weight of N is 20 kg.

Summary of Weights

Based on the calculations, we can list the weights of all objects:

Checking the relationships:

• L (40 kg) is twice N (20 kg): \(40 = 2 \times 20\), Correct.
• O (120 kg) is thrice L (40 kg): \(120 = 3 \times 40\), Correct.
• K (60 kg) is half O (120 kg): \(60 = 0.5 \times 120\), Correct.
• K (60 kg) is equal to M (60 kg): \(60 = 60\), Correct.

The calculations are consistent with all the given conditions.

Conclusion

Following the steps using the given weight relationships, we found that the weight of N is 20 kg.

Revision Table: Object Weights

Additional Information: Solving Word Problems

Word problems involving relationships like weights, ages, or distances can often be solved by following these steps:

1. Read Carefully: Understand what information is given and what needs to be found.
2. Assign Variables: Represent the unknown quantities with letters (like N for weight of N).
3. Write Equations: Translate the word relationships into mathematical equations.
4. Solve Equations: Use algebraic methods or substitution to solve for the unknown variables. Start with relationships where a value is given or where a variable can be directly determined.
5. Check Your Answer: Plug the values you found back into the original word problem or equations to make sure they hold true.

In this problem, we started with the known weight of M and the relationship \(K=M\), which allowed us to find K. Then, we used the relationships involving K and O, O and L, and finally L and N to find the weight of N step by step. This systematic approach is key to solving such problems accurately.