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24 Oct 2024, 17:04
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Zinc: 16
Mix B: 48
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (03:19) correct
65%
(03:29)
wrong
based on 488
sessions
History
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Not Attempted Yet
Brass is an alloy of copper and zinc whose proportions can vary to achieve different properties. Mix A, which weighs 50 kg, consists of 66% copper and 34% zinc in one such blend. This mix must be adjusted to increase its hardness by adding the maximum possible amount of zinc while ensuring that the zinc content does not exceed the weight of the copper in the new mix. Another blend, Mix B, contains 40% copper and 60% zinc and can be combined with Mix A to achieve the desired proportion.
Select the weight of pure zinc in kg that would be added by combining Mix A with either zinc alone or with Mix B to meet the above requirement. Make only two selections, one from each column.
Select the weight of pure zinc in kg that would be added by combining Mix A with either zinc alone or with Mix B to meet the above requirement. Make only two selections, one from each column.
| Zinc | Mix B | |
| 8 | ||
| 16 | ||
| 32 | ||
| 48 | ||
| 50 | ||
| 72 |
ShowHide Answer
Official Answer
Zinc: 16
Mix B: 48
General Discussion
25 Oct 2024, 00:00
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1. We are asked to find the maximum weight of zinc that was added (without breaking the requirement) after doing a method - either adding only zinc or adding Mix B.
2. It is known that amount of copper in Mix A is 66% of 50kg or 33kg and the amount of zinc in Mix A is 50-33 = 17kg. Our requirement states that the total amount of copper is greater than or equal to the total amount of zinc.
3. Let’s consider both methods:
2. It is known that amount of copper in Mix A is 66% of 50kg or 33kg and the amount of zinc in Mix A is 50-33 = 17kg. Our requirement states that the total amount of copper is greater than or equal to the total amount of zinc.
3. Let’s consider both methods:
- [color=#000000][size=100]Method 1: Pure Zinc. Since no copper is added, the amount of copper will be 33 kg. Let the amount of pure zinc added be Z. Then the total amount of zinc (the maximum that there can be) will be equal to 17+Z = 33 -> Z = 16 kg. So, our answer will be 16.[/size][/color]
- [color=#000000][size=100]Method 2: Mix B. Mix B contains 40% copper and 60% zinc. To balance the mix, if B kg of Mix B is added, then 0.6B will be added to the existing 17 kg of zinc. Then the total amount of zinc (the maximum that there can be) will be equal to 17 + 0.6B = 33+0.4B -> 0.2B = 16 -> B = 80. This means that the amount of zinc added 0.6B = 0.6*80 = 48. So, our answer will be 48.[/size]
[/color]
