MathDB

22

Part of 2006 AMC 10

Problems(2)

Pig and goat currency

Source: AMC 12 2006A, Problem 14

2/5/2006
Two farmers agree that pigs are worth $300 \$300 and that goats are worth $210 \$210. 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 \$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? <spanclass=′latex−bold′>(A)</span>$5<spanclass=′latex−bold′>(B)</span>$10<spanclass=′latex−bold′>(C)</span>$30<spanclass=′latex−bold′>(D)</span>$90<spanclass=′latex−bold′>(E)</span>$210 <span class='latex-bold'>(A) </span> \$5\qquad <span class='latex-bold'>(B) </span> \$10\qquad <span class='latex-bold'>(C) </span> \$30\qquad <span class='latex-bold'>(D) </span> \$90\qquad <span class='latex-bold'>(E) </span> \$210
rationumber theorygreatest common divisorAMC
Elmo's Sandwiches

Source: AMC 12 2006B, Problem 14

2/17/2006
Elmo makes N N sandwiches for a fundraiser. For each sandwich he uses B B globs of peanut butter at 4 cents per glob and J J blobs of jam at 5 cents per glob. The cost of the peanut butter and jam to make all the sandwiches is $ \$2.53. Assume that B,J, B, J, and N N are all positive integers with N>1 N > 1. What is the cost of the jam Elmo uses to make the sandwiches? <spanclass=′latex−bold′>(A)</span>$1.05<spanclass=′latex−bold′>(B)</span>$1.25<spanclass=′latex−bold′>(C)</span>$1.45<spanclass=′latex−bold′>(D)</span>$1.65<spanclass=′latex−bold′>(E)</span>$1.85 <span class='latex-bold'>(A) </span> \$1.05 \qquad <span class='latex-bold'>(B) </span> \$1.25 \qquad <span class='latex-bold'>(C) </span> \$1.45 \qquad <span class='latex-bold'>(D) </span> \$1.65 \qquad <span class='latex-bold'>(E) </span> \$1.85
AMC