2010 AMC 10B Problems/Problem 24
Problem
Solution
Represent the teams' scores as: and
We have Manipulating this, we can get , or
Since both are increasing sequences, . We can check cases up to because when , we get . When
Checking each of these cases individually back into the equation , we see that only when a=5 and n=2, we get an integer value for m, which is 9. The original question asks for the first half scores summed, so we must find
See also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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All AMC 10 Problems and Solutions |