perplexus.info :: Numbers : Three Pasture Puzzle

Three Pasture Puzzle (Posted on 2022-06-01)

Bernie has three pastures, each containing an equal number of animals. He sold all the animals of his pastures to 37 persons, each buying an equal number of animals.

If the cows cost $32.00 each, goats $15.00 each and pigs $5.00 each - determine the maximum number of animals Bernie could have, if he received $1661.00 from the sale.

No Solution Yet Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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re(2): Solution

| Comment 3 of 8 |

(In reply to re: Solution by Steve Herman)

Steve: Ah yes.

So in the mod 5 world, cows cost 2 mod 5, others cost 0 mod 5 and the total dollar amount is 1 mod 5. So 3 cows is 1 mod 5.

(3,0,313) is $1661 but 316 animals

If you add one goat (@$15) and subtract 3 pigs(@$5), the dollars remain the same but the animal count drops by 2.

So add 47 goats and subtract 3*47 = 141 pigs to decrease animals by 2*47 = 94

(3,47,172) is $1661 and 222 animals

Posted by Larry on 2022-06-01 12:30:49

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