Logic Puzzle # 148 Logic Problems Help

Logic Problem Solution:
"Jeopardy!"

From the introduction, the three ended up with a total of \$17,000 after going into "Final Jeopardy!" with a total of \$13,000 (clue 5). By clue 1, in the final round, Ben doubled his money and McNabb added \$2,000, but the Summerset contestant lost 1/3 of his or her winnings. By clue 4, Laurel finished third with \$4,000 in winnings; she is McNabb or the Summerset resident in clue 1. If she were McNabb, Laurel then would have had \$2,000 after "Double Jeopardy!" (1). In clue 5, then, we would have Ben + Summerset + 2,000 = 13,000, or Ben + Summerset = 11,000; and in clue 1, we would have 2*Ben + 2/3*Summerset + 4,000 = 17,000, or 2*Ben + 2/3*Summerset = 13,000. Solving, we double the first equation and subtract the second

2*Ben + 2  *Summerset =  22,000
-2*Ben - 2/3*Summerset = -13,000
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1 1/3*Summerset =     9,000

So the person from Summerset would have had \$6,750 after "Double Jeopardy!" and \$4,500 after "Final Jeopardy!", with Ben having \$4,250 and \$8,500 after those two rounds and being the winner. But by clue 2, the second place contestant would have had \$5,500--no, Laurel would have had \$4,000 and the Summerset contestant \$4,500. Therefore, Laurel is the one from Summerset. Since she ended up with \$4,000 (4) after losing 1/3 in "Final Jeopardy!" (1), she would have had \$6,000 going into the final round. In clue 5, then, we would have Ben + McNabb + 6,000 = 13,000, or Ben + McNabb = 7,000; and in clue 1, we would have 2*Ben + McNabb + 2,000 + 4,000 (Laurel) = 17,000, or 2*Ben + McNabb = 11,000. Solving, we double the first equation and subtract the second

2*Ben + 2*McNabb =  14,000
-2*Ben -      McNabb = -11,000
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McNabb =    3,000

So McNabb would have had \$3,000 and \$5,000 after "Double Jeopardy!" and "Final Jeopardy!" respectively, and Ben would have had \$4,000 and \$8,000. McNabb is Jay. By clue 2, Laurel is Hardy and Ben Chance. Ben is from Peyton Park and Jay from Thoreau Falls (3). The contestants on the TV favorite finished as follows:

• Ben Chance, Peyton Park, \$8,000
• Jay NcNabb, Thoreau Falls, \$5,000
• Laurel Hardy, Summerset, \$4,000