There are 150 weights. Some are 1 kg weights and some are 2 kg weights. The…
2025
There are 150 weights. Some are 1 kg weights and some are 2 kg weights. The sum of the weights is 260 kg.What is the number of 1kg weights?
Answer: D. 40 — Step-by-Step SolutionTo find the number of 1 kg weights, we can set up a system of linear equations based on the total count of weights and their total mass.…
- A.
70
- B.
55
- C.
50
- D.
40
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Correct answer: D
Step-by-Step Solution
To find the number of 1 kg weights, we can set up a system of linear equations based on the total count of weights and their total mass.
Define the variables:
Let A be the number of 1 kg weights.
Let B be the number of 2 kg weights.
Set up the equations:
Total number of weights: A + B = 150
Total mass of weights: 1 * A + 2 * B = 260
Solve the system of equations:
From the first equation, we know B = 150 - A.
Substitute this into the second equation: A + 2 * (150 - A) = 260 A + 300 - 2A = 260 -A + 300 = 260 -A = 260 - 300 -A = -40 A = 40