SOLUTION: Aliaba was arranging the carpets for the flying carpet brigade. They were going to fly in a rectangular formation. When he put 4 carpets in each row, he had 3 left over. When he

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Question 460663: Aliaba was arranging the carpets for the flying carpet brigade. They were going to fly in a rectangular formation. When he put 4 carpets in each row, he had 3 left over. When he put 5 carpets in each row, he had 1 left over. How many carpets could there have been in the carpet brigade?
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Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


To find the minimum number that has the characteristic that and set:



And solve. It should then be casual to the most obvious observer that since 4 times 5 is 20, that if you add any multiple of 20 to 11 you will get the same result.

Now we need to find a value such that is non-prime. That way, we can find a pair of integer factors and arrange the carpets in a rectangle with none left over.

11 is prime

31 is prime

51 NOT prime. 3 times 17 is a possible solution

71 is prime

91 NOT prime. 7 times 13...

There are infinitely more.

John

My calculator said it, I believe it, that settles it
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