Difference between revisions of "2000 AMC 12 Problems/Problem 12"
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:<math>(A + 1)(M + 1)(C + 1) = A \cdot M \cdot C + A \cdot M + M \cdot C + A\cdot C + 13</math> | :<math>(A + 1)(M + 1)(C + 1) = A \cdot M \cdot C + A \cdot M + M \cdot C + A\cdot C + 13</math> | ||
− | The [[term]] <math>(A + 1)(M + 1)(C + 1)</math> is [[maximum|maximized]] when A, M, and C are | + | The [[term]] <math>(A + 1)(M + 1)(C + 1)</math> is [[maximum|maximized]] when A, M, and C are close together, which in this case would be if all of them were 4. Thus, |
:<math>125 = A \cdot M \cdot C + A \cdot M + M \cdot C + A\cdot C + 13</math> | :<math>125 = A \cdot M \cdot C + A \cdot M + M \cdot C + A\cdot C + 13</math> |
Revision as of 18:18, 4 March 2007
Problem
Let A, M, and C be nonnegative integers such that . What is the maximum value of +++?
Solution
The term is maximized when A, M, and C are close together, which in this case would be if all of them were 4. Thus,
See also
2000 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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 |