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28 Jan 2024, 11:05
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A
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A batch of fresh grapes is fully dried to make raisins by 2 sequential processes. The first drying process is in the open air and results in partially dried grapes that have a weight 65% less than the weight of the fresh grapes. The partially dried grapes are then placed in a dehydrating device, making raisins that have a weight 45% less than the weight of the partially dried grapes. No other changes in weight occur. Which of the following expressions gives the value of k such that, if k kilograms of fresh grapes are fully dried, then the total weight of the resulting raisins is exactly 1 kilogram?
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
2024-01-28_21-58-34.png [ 95.43 KiB | Viewed 4814 times ]
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
Attachment:
2024-01-28_21-58-34.png [ 95.43 KiB | Viewed 4814 times ]
28 Jan 2024, 11:07
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guddo
A batch of fresh grapes is fully dried to make raisins by 2 sequential processes. The first drying process is in the open air and results in partially dried grapes that have a weight 65% less than the weight of the fresh grapes. The partially dried grapes are then placed in a dehydrating device, making raisins that have a weight 45% less than the weight of the partially dried grapes. No other changes in weight occur. Which of the following expressions gives the value of k such that, if k kilograms of fresh grapes are fully dried, then the total weight of the resulting raisins is exactly 1 kilogram?
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
Attachment:
2024-01-28_21-58-34.png
From k kilograms of fresh grapes, we get \(k(1 - 0.65)(1 - 0.45) = k(0.35)(0.55)\) kilograms of raisins.
We need this to be exactly 1 kilogram, hence \(k(0.35)(0.55) = 1\), which results in \(k=\frac{1}{(0.35)(0.55)}\).
Answer: A.
28 Jan 2024, 13:22
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guddo
A batch of fresh grapes is fully dried to make raisins by 2 sequential processes. The first drying process is in the open air and results in partially dried grapes that have a weight 65% less than the weight of the fresh grapes. The partially dried grapes are then placed in a dehydrating device, making raisins that have a weight 45% less than the weight of the partially dried grapes. No other changes in weight occur. Which of the following expressions gives the value of k such that, if k kilograms of fresh grapes are fully dried, then the total weight of the resulting raisins is exactly 1 kilogram?
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
A. \(\frac{1}{(0.35)(0.55)}\)
B. \(\frac{1}{(0.45)(0.65)}\)
C. \(\frac{1 + 0.45}{0.65}\)
D. \(\frac{1 + 0.65}{0.45}\)
E. \(\frac{1}{1 - (0.35)(0.55)}\)
Attachment:
2024-01-28_21-58-34.png
Process 1
The first drying process is in the open air and results in partially dried grapes that have a weight 65% less than the weight of the fresh grapes.
Weight of the grapes after the drying process = \(\frac{100-65}{100} * k = 0.35k\)
Process 2
The partially dried grapes are then placed in a dehydrating device, making raisins that have a weight 45% less than the weight of the partially dried grapes
Weight of the grapes after the dehydrating process = \(\frac{100-45}{100} * 0.35k = 0.55 * 0.35k\)
Given
\(0.55 * 0.35 * k = 1\)
\(k = \frac{1}{0.55 * 0.35}\)
Option A
