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26 Nov 2024, 08:00
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A: 150
B: 168
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
84% (02:32) correct
16%
(03:04)
wrong
based on 392
sessions
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Not Attempted Yet
A chemist is mixing two powders, X and Y, to create an alloy. The final alloy must contain a specific ratio of X to Y for structural integrity. Two potential ratios are being tested:
The chemist starts with 90 grams of X and 80 grams of Y. The goal is to use the maximum amount of both powders without exceeding either supply.
Based on the above information, select for A the amount of the alloy that can be produced using Ratio A and for B the amount of the alloy that can be produced using Ratio B.
- Ratio A: 3 grams of X to 2 grams of Y
- Ratio B: 11 grams of X to 10 grams of Y
The chemist starts with 90 grams of X and 80 grams of Y. The goal is to use the maximum amount of both powders without exceeding either supply.
Based on the above information, select for A the amount of the alloy that can be produced using Ratio A and for B the amount of the alloy that can be produced using Ratio B.
| A | B | |
| 142 | ||
| 150 | ||
| 157 | ||
| 165 | ||
| 168 | ||
| 174 |
ShowHide Answer
Official Answer
A: 150
B: 168
27 Nov 2024, 11:00
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1. We are asked to figure out the maximum amount of alloy that can be made using each of the possible ratios.
2. The problem is that we don’t know which powder will be used up first. To figure this out, we can compare the ratio of X to Y. Originally, we have ratio of 90:80 or 1.125.
3. Now let’s find how much powder will be used altogether, as this should be the mass of the alloy.
2. The problem is that we don’t know which powder will be used up first. To figure this out, we can compare the ratio of X to Y. Originally, we have ratio of 90:80 or 1.125.
- Ratio A: 3:2 = 1.5 > 1.125. So, X will be used up first. This means that Ratio A will be used 90/3 = 30 times.
- Ratio B: 11:10 = 1.1 < 1.125. So, Y will be used first. This means that Ratio B will be used 80/10 = 8 times.
3. Now let’s find how much powder will be used altogether, as this should be the mass of the alloy.
- Ratio A: Is used 30 times, so 3*30 = 90 grams of X and 2*30 = 60 grams of Y. 90 + 60 = 150 grams of the alloy.
- Ratio B: Is used 8 times, so 11*8 = 88 grams of X and 10*8 = 80 grams of Y. 88 + 80 = 168 grams of the alloy.
14 Feb 2025, 00:25
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here as we can see the ratio for A = 3:2 , which means for every 3 grams of x there would be 2 grams of y, so of 90g x we can make 30 parts of 3 grams of x and of 80g of y we can make 40 parts of 2 grams of y, so summing up 30x3 + 30x2 = ( here we can't take all 40 parts because only 30 parts of x are available) , hence 150 for ratio A,
Similarly for ratio B we get 8 parts of x and 8 parts of y, there for 8x11 + 8x10 = 168 for ratio B
Similarly for ratio B we get 8 parts of x and 8 parts of y, there for 8x11 + 8x10 = 168 for ratio B
