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| ==Problem==
| | #redirect[[2023 AMC 12A Problems/Problem 8]] |
| 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?
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| <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>\frac{ax+11}{a+1} = x+1</math> and <math>\frac{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>. The answer is \boxed{\textbf{(B) }7}
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| ~walmartbrian ~Shontai ~andyluo
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| ==See Also==
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| {{AMC10 box|year=2023|ab=A|num-b=9|num-a=11}}
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| {{MAA Notice}}
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