Browse · MATH
Printjmc
number theory senior
Problem
Two farmers agree that pigs are worth \300\. 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 \390$ 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?
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, and no positive debt less than \30\boxed{\30} can be resolved since This is done by giving 3 goats and receiving 2 pigs.
Final answer
\$30