WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD   Session II: SEVENTH GRADE ALGEBRAIC SENSE   Make sure you include proper units in your answer! 7

1.   Carl's hands trembled as he stood in front of the safe and unfolded the crumpled piece of paper holding the combination that would open the safe.   "Rats!" he moaned.   The combination consisted of three numbers.   The last number was written in the form of a riddle which read: "2/3 of the last number, added to 16, will equal two times as much as the last number."   What is the last number in the combination?

2.   The Tripoli Triathlon has ended.   The contestants, who had trained long for this event, all came hoping to win.   But only the best remained in the competition to the end.   The judges noticed something very interesting as the contestants crossed the finish line.   There were one first-place winner, two second-place winners, and three third-place winners.   If that pattern continued, in what place would be the 200th person who crossed the finish line?

3.   How many ways can someone make \$2.43 with 5 cent and 8 cent stamps?

4.   Twelve people rent a boat.   By taking 8 more people (at the same rental rate), the cost to each person is reduced by \$2.50.   How much is the rent for the boat?

5.   Find a four-digit number abcd such that if a decimal point is placed between ab and cd, (i.e., ab.cd), the resulting number is the mean of ab and cd.