Difference between revisions of "2006 AMC 12A Problems/Problem 14"
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Two farmers agree that pigs are worth <math>$300</math> and that goats are worth <math>$210</math>. 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 <math>$390</math> 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? | Two farmers agree that pigs are worth <math>$300</math> and that goats are worth <math>$210</math>. 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 <math>$390</math> 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? | ||
| − | <math> \mathrm{(A) \ } $5\qquad \mathrm{(B) \ } $10\qquad \mathrm{(C) \ } $30\qquad \mathrm{(D) \ } $90 | + | <math> \mathrm{(A) \ } $5\qquad \mathrm{(B) \ } $10\qquad \mathrm{(C) \ } $30\qquad \mathrm{(D) \ } $90</math><math>\mathrm{(E) \ } $210</math> |
== Solution == | == Solution == | ||
Revision as of 23:55, 10 July 2006
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?
$\mathrm{(A) \ } $5\qquad \mathrm{(B) \ } $10\qquad \mathrm{(C) \ } $30\qquad \mathrm{(D) \ } $90$ (Error compiling LaTeX. Unknown error_msg)$\mathrm{(E) \ } $210$ (Error compiling LaTeX. Unknown error_msg)
