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Kevin,
Tuesday, October 1, 2024
"4x pumpkins bought for $20x
6y pumpkins bought for $20y
4x = 6y so x = 1.5y
Total pumpkins bought = 4x + 6y = 6y + 6y = 12y
Total cost = 20x + 20y = 20(x + y) = 20(1.5y + y) = 20(2.5y)
12y pumpkins cost $20(2.5y)
$20 buys (on average) 12y/2.5y = 4.8 pumpkins "
Chris,
Tuesday, October 1, 2024
"The way I read the puzzle, Vesper buys a number of pumpkins that is a multiple of 4 and a multiple of 6 (my solution can be tweaked if that’s not the case…). That means that the number of pumpkins purchased in each shop must also be a multiple of 12, so let’s call that number 12a, where a is a positive integer.
In the first shop Vesper buys 12a pumpkins at a price of 20/4 each. So it cost him 12a * 20/4 = 60a altogether.
In the second shop Vesper buys 12a pumpkins at a price of 20/6 each. So this cost him 12a * 20/6 = 40a.
Vesper bought 24a pumpkins for £100a.
£100a = 24a pumpkins.
if we divide both sides of this by 5a we get the answer to the puzzle:
£20 = 4.8 pumpkins
The mean number of pumpkins bought for £20 is 4.8 pumpkins. "