Difference between revisions of "2001 AMC 12 Problems/Problem 4"
m (→Solution) |
Pidigits125 (talk | contribs) |
||
Line 1: | Line 1: | ||
+ | {{duplicate|[[2001 AMC 12 Problems|2001 AMC 12 #4]] and [[2001 AMC 10 Problems|2002 AMC 10A #16]]}} | ||
+ | |||
== Problem == | == Problem == | ||
The mean of three numbers is <math>10</math> more than the least of the numbers and <math>15</math> | The mean of three numbers is <math>10</math> more than the least of the numbers and <math>15</math> |
Revision as of 17:34, 16 March 2011
- The following problem is from both the 2001 AMC 12 #4 and 2002 AMC 10A #16, so both problems redirect to this page.
Problem
The mean of three numbers is more than the least of the numbers and less than the greatest. The median of the three numbers is . What is their sum?
Solution
Let be the mean of the three numbers. Then the least of the numbers is and the greatest is . The middle of the three numbers is the median, 5. So , which implies that . Hence, the sum of the three numbers is , and the answer is .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |