Braingle: 'Farmers market' Brain Teaser

Farmers market

Math brain teasers require computations to solve.

Puzzle ID:	#403
Fun:	(2.56)
Difficulty:	(2.27)
Category:	Math
Submitted By:	Andy
Corrected By:	Mogmatt16

A farmer must spend exactly $100 to buy exactly 100 animals, and must buy at least one of each animal. Cows are $10 each, Goats are $1 each and Chickens are 8 for a $1. What does he buy?

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Comments

(user deleted) Nov 21, 2001	not my farmer he couldn't be bothered with all the math and bought 100 goats
bluetwo May 29, 2002	do you know how many different possible answers there are to this question? i haven't added it up, but there are quite a few...
dewtell Jul 31, 2002	Actually, there are exactly two answers (the two given). The number of cows must be a multiple of 7, and the number of chickens must be 72/7 times the number of cows. 7 cows gives you the first answer; 0 cows gives you petera's answer.
canu Jul 13, 2004	Do some people have trouble reading, or was "and must buy at least one of each animal" added to the teaser after Jul 31, 2002?
Jimbo Mar 16, 2005	How about a full solution?
Maslin Jun 09, 2005	I totally missed the must buy one of each animal. So I chose 100 goats. Good one!
JessicaLynn Mar 24, 2006	Couldn't you buy 9 cows, 9 goats and 8 chickens?
JessicaLynn Mar 24, 2006	never mind, I skipped the 100 animals part.
rrn0rrnrrnY Sep 11, 2006	i came up with the same answer without a calculator and enjoyed its simplicity, it may have other solutions but i enjoyed this just the way it was
cowman12 Jan 11, 2007	Good one! I wish I had 7 cows.
ciotog Feb 11, 2007	Here's the logic: First, forget about the goats for now - each goat contributes 1 to the total # of animals and 1 to the cost, so they're trivial Let 'a' be the number of cows, and 'b' be the number of chickens. For the total cost and the number of animals to be equal, then: 10a + (1/b = a + b == 80a + b = 8a + 8b == 72a = 7b which means there has to be 72/7 times as many chickens as cows, and 7/72 times as many cows as chickens. The only way to have this and have the totals to be greater than 0 and less than 100 would be to have 72 chickens and 7 cows. Let the number of goats bring the totals up to 100.
ciotog Feb 11, 2007	Naturally (1/ should be ( 1/8 )
javaguru Jan 30, 2009	Easier way to explain the logic: The digital sum (sum of the two digits) of the number of chickens must equal the cost of the chickens. 7 + 2 = 9; 9 x 8 = 72. Then buy the number of cows represented by the first digit in the number of chickens. This will give you the same number of animals as dollars spent, allowing the remainder to be spent on goats.