Question
A factory produces three alloys: X (30% copper), Y (50%
copper), and Z (70% copper). An engineer combines these alloys in the ratio 3:2:1. If the total weight of the mixture is 120 kg, calculate the percentage of copper in the resulting mixture.Solution
Let the weights of Alloy X, Y, and Z be 3x, 2x, and x kg, respectively. Total weight = 3x + 2x + x = 6x = 120 kg Thus, x = 20 kg Weights of alloys: Alloy X: 3 × 20 = 60 kg Alloy Y: 2 × 20 = 40 kg Alloy Z: 1 × 20 = 20 kg Copper content: Alloy X: 60 × 0.30 = 18 kg Alloy Y: 40 × 0.50 = 20 kg Alloy Z: 20 × 0.70 = 14 kg Total copper content = 18 + 20 + 14 = 52 kg Total weight of mixture = 120 kg Percentage of copper = (52 / 120) × 100 = 43.33% The percentage of copper in the final mixture is 43.33%.
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