You are sent to the market by your father with 800 dollars, and told to buy 100 animals. When you arrive at the market, you find out that pigs cost 8 dollars each, so it would be easy to follow your father's instructions.

However, you see that there are only 99 pigs for sale. The only other animals there are chickens for 1 dollar each, and cows for 80 dollars each.

If there are enough chickens and cows for you to buy as many as you wanted, how can you end up buying 100 animals using exactly 800 dollars?

(1) 8p+ch+80c= 800 dollars
(2) p+ch+c=100 animals

Multiply Equation(2) by 8:
(3) 8p+8ch+8c=800
Subtract (1)from (3) and solve for ch: ch= 72c/7.
Since ch must be an integer and 72 is not divisible by 7, c must be either 7, 14, 21, etc.
but only 7 gives a ch less than 100 as required by Eq.(2).
The answer is 72 chickens, 21 pigs, 7 cows.

Posted by sizz on 2004-02-21 04:07:03