Difference between revisions of "1993 AIME Problems/Problem 3"
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== Problem == | == Problem == | ||
| + | The table below displays some of the results of last summer's Frostbite Falls Fishing Festival, showing how many contestants caught <math>n\,</math> fish for various values of <math>n\,</math>. | ||
| + | |||
| + | <table border="1"> | ||
| + | <tr><td><math>n\,</math></td><td><math>0\,</math></td><td><math>1\,</math></td><td><math>2\,</math></td><td><math>3\,</math></td><td><math>\dots\,</math></td><td><math>13\,</math></td><td><math>14\,</math></td><td><math>15\,</math></td></tr> | ||
| + | <tr><td><math>\mbox{number of contestants who caught }n\mbox{ fish}\,</math></td><td><math>9\,</math></td><td><math>5\,</math></td><td><math>7\,</math></td><td><math>23\,</math></td><td><math>\dots\,</math></td><td><math>5\,</math></td><td><math>2\,</math></td><td><math>1\,</math></td></tr> | ||
| + | </table> | ||
| + | |||
| + | In the newspaper story covering the event, it was reported that | ||
| + | |||
| + | (a) the winner caught 15 fish; | ||
| + | |||
| + | (b) those who caught 3 or more fish averaged 6 fish each; | ||
| + | |||
| + | (c) those who caught 12 or fewer fish averaged 5 fish each. | ||
| + | |||
| + | What was the total number of fish caught during the festival? | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1993|num-b=2|num-a=4}} | |
Revision as of 11:46, 26 March 2007
Problem
The table below displays some of the results of last summer's Frostbite Falls Fishing Festival, showing how many contestants caught 
fish for various values of .
|  |  |  |  |  |  |  |  |
 |  |  |  |  | | | | |
In the newspaper story covering the event, it was reported that
(a) the winner caught 15 fish;
(b) those who caught 3 or more fish averaged 6 fish each;
(c) those who caught 12 or fewer fish averaged 5 fish each.
What was the total number of fish caught during the festival?
Solution
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See also
| 1993 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
