Difference between revisions of "1991 AJHSME Problems/Problem 19"
5849206328x (talk | contribs) (Created page with '==Problem== The average (arithmetic mean) of <math>10</math> different positive whole numbers is <math>10</math>. The largest possible value of any of these numbers is <math>\…') |
|||
Line 17: | Line 17: | ||
{{AJHSME box|year=1991|num-b=18|num-a=20}} | {{AJHSME box|year=1991|num-b=18|num-a=20}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 23:07, 4 July 2013
Problem
The average (arithmetic mean) of different positive whole numbers is . The largest possible value of any of these numbers is
Solution
If the average of the numbers is , then their sum is .
To maximize the largest number of the ten, we minimize the other nine. Since they must be distinct, positive whole numbers, we let them be . Their sum is .
The sum of nine of the numbers is , and the sum of all ten is so the last number must be .
See Also
1991 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.