(1) Three teams -- Handley, James Wood, and
Sherando -- compete in the City-County Track
meet. The meet has ten events.
(2) Each event has one first place winner, one second place winner and one third place winner.
(3) Three points and a gold medal are awarded for
each first place.
Two points and a silver medal are awarded for
each second place.
One point and a bronze medal are awarded for
each third place.
Gold Medals |
Silver Medals |
Bronze Medals |
Total Medals |
Total Points |
|
Handley | |||||
James Wood | |||||
Sherando |
Solution to the Problem:
(1) Clue #4 gives us information about the gold medals:Sherando > Handley and Sherando > Wood means that Sherando won at least 4 gold medals. (2) Clue #5 gives us the following equation for total medals:
Sherando = Wood + 1 = Handley + 2 (3) Clue #6 gives us the following equation for total points:
Handley = Wood + 1 = Sherando + 2 (4) With 10 events, there must be 60 points, and from the previous statement, Handley scored 21, Wood 20, and Sherando 19. (5) With ten events, there must be 30 medals, so Sherando got 11, Wood 10, and Handley 9. (6) Now you should be able to fill in the table:
Gold Medals |
Silver Medals |
Bronze Medals |
Total Medals |
Total Points |
|
Handley | 3 | 6 | 0 | 9 | 21 |
James Wood | 3 | 4 | 3 | 10 | 20 |
Sherando | 4 | 0 | 7 | 11 | 19 |
Correctly solved by:
1. Todd Lewis | Winchester, VA |
2. Dante DeFazio | Winchester, VA |
3. Jia Ran | Rome, Italy |
4. Jeremy Ramsey | Stephens City, VA |
5. Darren Rennie | Winchester, VA |
6. Bob Hearn | Winchester, VA |
7. Ginger Anderson | Winchester, VA |