What are the silicon percentages of the two different alloys combined to create a sample that is 50.0% silicon?

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Multiple Choice

What are the silicon percentages of the two different alloys combined to create a sample that is 50.0% silicon?

Explanation:
The key idea is that the final silicon percentage in a mixture is a weighted average of the two alloys’ percentages, based on how much of each alloy you use. If you mix an alloy with 30% silicon and another with 80% silicon, you can reach exactly 50% by choosing the right amounts. For example, use 3 units of the 30% alloy and 2 units of the 80% alloy. The total silicon is 3×30 + 2×80 = 90 + 160 = 250, and the total mass is 5 units, so the mixture is 250/5 = 50% silicon. This shows why 30% and 80% can produce a 50% result. Any pair that brackets 50% can work with a suitable mass ratio, but the given combination demonstrates a straightforward ratio (3:2) that yields the target.

The key idea is that the final silicon percentage in a mixture is a weighted average of the two alloys’ percentages, based on how much of each alloy you use.

If you mix an alloy with 30% silicon and another with 80% silicon, you can reach exactly 50% by choosing the right amounts. For example, use 3 units of the 30% alloy and 2 units of the 80% alloy. The total silicon is 3×30 + 2×80 = 90 + 160 = 250, and the total mass is 5 units, so the mixture is 250/5 = 50% silicon. This shows why 30% and 80% can produce a 50% result.

Any pair that brackets 50% can work with a suitable mass ratio, but the given combination demonstrates a straightforward ratio (3:2) that yields the target.

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