A man wishes to sell a puppy for $11. A customer wants to buy it but only has foreign currency. The exchange rate for the foreign currency is 11 round coins = $15, 11 square coins = $16, 11 triangular coins = $17.

How many of each coinage should the customer pay?

Well, this is my solution.

Since 11 round coins equal $15, each coin is $15/11. Likewise, the square coins are $16/11, and the triangular coins are $17/11. The amount we're trying to get is 11 dollars, or 121/11.

To get the number 121 from all these numbers, I divided by 16. 121=8*16-7=7*16+9. So, to get 121, we can use coins of lesser or greater value to compensate for the remainders. Therefore, only combination that works is 7 round coins and a square coin. You cannot change 9 of the coins to triangular coins because there are only seven coins using that combination.

Posted by Tristan on 2003-10-31 16:42:41