Thursday, August 2, 2007

He should just go to Sam's Club

Tonight's final question:
A butcher goes to market. The market sells cows for $15 each, geese for $1 each, and chickens for 25 cents each. The butcher buys exactly 100 animals, and spends exactly $100. If he bought at least one cow, one goose, and one chicken, how many of each animal did he buy?


anne57 said...

3 cows
41 geese
56 chickens

J. Bowman said...

For those wondering where that answer comes from:
We're looking for a combination that averages a dollar per animal. Since the geese actually are a dollar each, the key is figuring out how many cows and chickens he bought. If x is the number of cows and y the number of chickens, then

15x + 0.25y = x + y

which works out to

14x = 0.75y


56x = 3y

Which means there are 3 cows for every 56 chickens, and since the number of chickens is an integer between 1 and 100, these must be the exact numbers, leaving us with 41 geese.