2023 AMC 12A Problems/Problem 8
Contents
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
Let 
represent the sum of Maureen's test scores previously and 
be the number of scores taken previously.
So, 
and 
We can use the first equation to write in terms of .
We then substitute this into the second equation: 
From here, we solve for t, getting 
.
We substitute this to get 
.
Therefore, the solution to the problem is 
~milquetoast
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 | |
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