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| − | Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an <math>11</math> on the next quiz, her mean will increase by <math>1</math>. If she scores an <math>11</math> on each of the next three quizzes, her mean will increase by <math>2</math>. What is the mean of her quiz scores currently?
| + | #redirect[[2023 AMC 12A Problems/Problem 8]] |
| − | <math>\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8</math>
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| − | ==Solution 1==
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| − | Let <math>a</math> represent the amount of tests taken previously and <math>x</math> the mean of the scores taken previously.
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| − | We can write the equation <math>(ax+11)/a+1 = x+1</math> and <math>(ax+33)/a+3 = x+2</math>.
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| − | Expanding, <math>ax+11 = ax+a+x+1</math> and <math>ax+33 = ax+2a+3x+6</math>.
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| − | This gives us <math>a+x = 10</math> and <math>2a+3x = 27</math>. Solving for each variable, <math>x=7</math> and <math>a=3</math>. (D)
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| − | ~walmartbrian ~Shontai ~andyluo
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