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08 Jan 2025, 03:47
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A parking lot contains 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average (arithmetic mean) weight of the vehicles in the lot is 3 tons. Assuming no cars leave the lot, how many trucks must leave to reduce the average weight of the remaining vehicles to 2 tons?
A. 5
B. 25
C. 30
D. 40
E. 45
A. 5
B. 25
C. 30
D. 40
E. 45
08 Jan 2025, 03:47
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Bookmarks
Official Solution:
A parking lot contains 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average (arithmetic mean) weight of the vehicles in the lot is 3 tons. Assuming no cars leave the lot, how many trucks must leave to reduce the average weight of the remaining vehicles to 2 tons?
A. 5
B. 25
C. 30
D. 40
E. 45
The current average weight of all vehicles is 3 tons. Cars weigh 1.5 tons, which is 1.5 tons below the average, while trucks weigh 3.5 tons, which is 0.5 tons above the average. To maintain this average, there must be three times as many trucks as cars. With a total of 60 vehicles, this gives 15 cars and 45 trucks.
We need to remove only trucks so that the average weight drops to 2 tons. Similarly, 2 tons is 0.5 away from the weight of cars (1.5 tons) and 1.5 away from the weight of trucks (3.5 tons). Therefore, after removing some number of trucks, there must be three times as many cars as trucks remaining.
Since there are 15 cars, the remaining number of trucks must be 15/3 = 5 trucks.
Thus, 45 - 5 = 40 trucks must leave the lot.
Answer: D
A parking lot contains 60 vehicles, a mix of cars and trucks. Each car weighs 1.5 tons, and each truck weighs 3.5 tons. The current average (arithmetic mean) weight of the vehicles in the lot is 3 tons. Assuming no cars leave the lot, how many trucks must leave to reduce the average weight of the remaining vehicles to 2 tons?
A. 5
B. 25
C. 30
D. 40
E. 45
The current average weight of all vehicles is 3 tons. Cars weigh 1.5 tons, which is 1.5 tons below the average, while trucks weigh 3.5 tons, which is 0.5 tons above the average. To maintain this average, there must be three times as many trucks as cars. With a total of 60 vehicles, this gives 15 cars and 45 trucks.
We need to remove only trucks so that the average weight drops to 2 tons. Similarly, 2 tons is 0.5 away from the weight of cars (1.5 tons) and 1.5 away from the weight of trucks (3.5 tons). Therefore, after removing some number of trucks, there must be three times as many cars as trucks remaining.
Since there are 15 cars, the remaining number of trucks must be 15/3 = 5 trucks.
Thus, 45 - 5 = 40 trucks must leave the lot.
Answer: D
09 Apr 2025, 02:44
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"To maintain this average, there must be three times as many trucks as cars." can you explain this part i did the question with traditional method took me 4 min.
Bunuel
