Difference between revisions of "1999 AMC 8 Problems/Problem 15"
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You can get at most <math>100</math> license plates total, giving an additional <math>100 - 60 = 40</math> plates, making the answer <math>\boxed {D}</math> | You can get at most <math>100</math> license plates total, giving an additional <math>100 - 60 = 40</math> plates, making the answer <math>\boxed {D}</math> | ||
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==See Also== | ==See Also== | ||
{{AMC8 box|year=1999|num-b=14|num-a=16}} | {{AMC8 box|year=1999|num-b=14|num-a=16}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:27, 11 November 2017
Contents
Problem
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set {C,H,L,P,R}, the second from {A,I,O}, and the third from {D,M,N,T}.
When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates that can be made by adding two letters?
Solution
Solution 1
There are currently choices for the first letter, choices for the second letter, and choices for the third letter, for a total of license plates.
Adding letters to the start gives plates.
Adding letters to the middle gives plates.
Adding letters to the end gives plates.
Adding a letter to the start and middle gives plates.
Adding a letter to the start and end gives plates.
Adding a letter to the middle and end gives plates.
You can get at most license plates total, giving an additional plates, making the answer
See Also
1999 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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.