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13 Mar 2025, 04:09
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A: 150
B: 168
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:
• 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.
• 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 |
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Official Answer
A: 150
B: 168
13 Mar 2025, 04:09
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Official Solution:
We are asked to figure out the maximum amount of alloy that can be made using each of the possible ratios.
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.
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.
Correct answer:
A "150"
B "168"
Bunuel
We are asked to figure out the maximum amount of alloy that can be made using each of the possible ratios.
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.
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.
Correct answer:
A "150"
B "168"
10 Jan 2026, 12:32
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Hi Bunuel,
Thanks for sharing the solution and explaining well.
I am struggling to approach these questions efficiently, could you share similar questions to practice and reinforce necessary fundamentals?
Thanks.
Thanks for sharing the solution and explaining well.
I am struggling to approach these questions efficiently, could you share similar questions to practice and reinforce necessary fundamentals?
Thanks.
Bunuel
