2007 AMC 10B Problems/Problem 16
- The following problem is from both the 2007 AMC 10B #16 and 2007 AMC 12B #12, so both problems redirect to this page.
Contents
Problem
A teacher gave a test to a class in which of the students are juniors and are seniors. The average score on the test was The juniors all received the same score, and the average score of the seniors was What score did each of the juniors receive on the ikd?
Solution
We can assume there are people in the class. Then there will be junior and seniors. The sum of everyone's scores is Since the average score of the seniors was the sum of all the senior's scores is The only score that has not been added to that is the junior's score, which is
Solution 2
Let the average score of the juniors be . The problem states the average score of the seniors is . The equation for the average score of the class (juniors and seniors combined) is . Simplifying this equation yields
~mobius247
See Also
2007 AMC 12B (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 |
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.