Difference between revisions of "2007 AMC 10B Problems/Problem 16"
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==Problem== | ==Problem== | ||
| − | A teacher gave a test to a class in which <math>10\%</math> of the students are juniors and <math>90\%</math> are seniors. The average score on the test was <math>84.</math> The juniors all received the same score, and the average score of the seniors was <math>83.</math> What score did each of the juniors receive on the | + | A teacher gave a test to a class in which <math>10\%</math> of the students are juniors and <math>90\%</math> are seniors. The average score on the test was <math>84.</math> The juniors all received the same score, and the average score of the seniors was <math>83.</math> What score did each of the juniors receive on the ikd? |
<math>\textbf{(A) } 85 \qquad\textbf{(B) } 88 \qquad\textbf{(C) } 93 \qquad\textbf{(D) } 94 \qquad\textbf{(E) } 98</math> | <math>\textbf{(A) } 85 \qquad\textbf{(B) } 88 \qquad\textbf{(C) } 93 \qquad\textbf{(D) } 94 \qquad\textbf{(E) } 98</math> | ||
Revision as of 08:23, 14 September 2022
- 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. 
