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11 Nov 2024, 06:29
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First mixture: 24
Final mixture: 40
Juanita combined two mixtures of lemonade. The first had 4 parts water to 1 part lime juice, and the second had 3 parts water to 2 parts lime juice. The final mixture contained 28% lime juice.
Select for First mixture the number of liters that could be in the first mixture, and for Final mixture the number of liters that could be in the final mixture that are jointly consistent with the given information. Make only two selections, one in each column.
Select for First mixture the number of liters that could be in the first mixture, and for Final mixture the number of liters that could be in the final mixture that are jointly consistent with the given information. Make only two selections, one in each column.
| First mixture | Final mixture | |
| 4 | ||
| 12 | ||
| 16 | ||
| 24 | ||
| 30 | ||
| 40 |
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Official Answer
First mixture: 24
Final mixture: 40
08 Jan 2025, 05:12
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GMATJoe716
0.2x + 0.4y = 0.28(x + y)
0.2x + 0.4y = 0.28x + 0.28y
0.12y = 0.08x
12y = 8x
3y = 2x
Hope it helps.
11 Nov 2024, 06:29
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Official Solution:
Since the first mixture had 4 parts water to 1 part lime juice, it contained 1/5 or 20% lime juice.
Since the second mixture had 3 parts water to 2 parts lime juice, it contained 2/5 or 40% lime juice.
Assuming the first mixture was \(x\) liters and the second was \(y\) liters, equating the amount of lime juice gives \(0.2x + 0.4y = 0.28(x + y)\), which simplifies to \(2x = 3y\).
Thus, the first mixture was \(x\) liters, and the final mixture was \(x + y = x + \frac{2x}{3} = \frac{5x}{3}\). The ratio of these quantities is \(x:\frac{5x}{3}=3:5\). Therefore, we are looking for options in a 3:5 ratio. Only 24 and 40 work.
Correct answer:
First mixture "24"
Final mixture "40"
Bunuel
Since the first mixture had 4 parts water to 1 part lime juice, it contained 1/5 or 20% lime juice.
Since the second mixture had 3 parts water to 2 parts lime juice, it contained 2/5 or 40% lime juice.
Assuming the first mixture was \(x\) liters and the second was \(y\) liters, equating the amount of lime juice gives \(0.2x + 0.4y = 0.28(x + y)\), which simplifies to \(2x = 3y\).
Thus, the first mixture was \(x\) liters, and the final mixture was \(x + y = x + \frac{2x}{3} = \frac{5x}{3}\). The ratio of these quantities is \(x:\frac{5x}{3}=3:5\). Therefore, we are looking for options in a 3:5 ratio. Only 24 and 40 work.
Correct answer:
First mixture "24"
Final mixture "40"
