Difference between revisions of "2023 AMC 12A Problems/Problem 8"
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Let <math>s</math> represent the sum of Maureen's test scores previously and <math>t</math> be the number of scores taken previously. | Let <math>s</math> represent the sum of Maureen's test scores previously and <math>t</math> be the number of scores taken previously. | ||
| − | So, <math>\frac{x+11}{n+1} = frac{x}{n}+1</math> | + | So, <math>\frac{x+11}{n+1} = \frac{x}{n}+1</math> |
==See Also== | ==See Also== | ||
Revision as of 22:50, 9 November 2023
Problem
Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 
on the next quiz, her mean will increase by 
. If she scores an on each of the next three quizzes, her mean will increase by 
. What is the mean of her quiz scores currently?
Solution 1
Let 
represent the amount of tests taken previously and 
the mean of the scores taken previously.
We can write the equations 
and 
.
Expanding, 
and 
.
This gives us 
and 
. Solving for each variable, 
and 
. The answer is 
~walmartbrian ~Shontai ~andyluo
Solution 2 (similar method to solution 1)
Let 
represent the sum of Maureen's test scores previously and 
be the number of scores taken previously.
So, 
See Also
| 2023 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 | ||
| 2023 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
