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