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2006 AMC 10A Problem 22

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2006 AMC 10A Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

Diophantine Equations · difficulty 4 of 5 · about 4 min · position P21-25

Two farmers agree that pigs are worth $300$ dollars and that goats are worth $210$ dollars. 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 $390$ dollar 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?

A)
$5$
B)
$10$
C)
$30$
D)
$90$
E)
$210$

2006 AMC 10A Problem 22

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