Difference between revisions of "2000 AIME II Problems/Problem 7"
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== Problem == | == Problem == | ||
| + | Suppose that <math>x,</math> <math>y,</math> and <math>z</math> are three positive numbers that satisfy the equations <math>xyz = 1,</math> <math>x + \frac {1}{z} = 5,</math> and <math>y + \frac {1}{x} = 29.</math> Then <math>z + \frac {1}{y} = \frac {m}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2000|n=II|num-b=6|num-a=8}} | |
Revision as of 18:12, 11 November 2007
Problem
Suppose that 
and 
are three positive numbers that satisfy the equations 
and 
Then 
where 
and 
are relatively prime positive integers. Find 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2000 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
