Problem:
Two farmers agree that pigs are worth and that goats are worth . When one farmer owes the other money, he pays the debt in pigs or goats, with "change" received in the form of goats or pigs as necessary. (For example, a debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If a debt of dollars can be resolved in this way, then integers and must exist with
As a consequence, must be a multiple of 30 , so no positive debt of less than can be resolved. A debt of can be resolved since
This is done by giving 3 goats and receiving 2 pigs.
The problems on this page are the property of the MAA's American Mathematics Competitions