2023 AMC 12A Problems/Problem 8: Difference between revisions
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We can use the first equation to write <math>s</math> in terms of <math>n</math>. | We can use the first equation to write <math>s</math> in terms of <math>n</math>. | ||
We then substitute this into the second equation: \pow{x}{n}+1$ | |||
==See Also== | ==See Also== | ||
Revision as of 22:53, 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, 
and 
We can use the first equation to write in terms of 
.
We then substitute this into the second equation: \pow{x}{n}+1$
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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