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2023 AMC 12A Problem 8

Problem 8 of 25EasierAlgebraProbability & Statistics

Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 1111 on the next quiz, her mean will increase by 1.1. If she scores an 1111 on each of the next three quizzes, her mean will increase by 2.2. What is the mean of her quiz scores currently?

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Solution

Let the current mean be mm over nn quizzes, so the total is S=mn.S=mn. Adding one 1111 gives mn+11n+1=m+1, \dfrac{mn+11}{n+1}=m+1, which simplifies to m+n=10.m+n=10. Adding three 1111’s gives mn+33n+3=m+2, \dfrac{mn+33}{n+3}=m+2, which simplifies to 3m+2n=27.3m+2n=27. Solving m+n=10m+n=10 and 3m+2n=273m+2n=27 gives m=7.m=7. Thus, the correct answer is D.
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Tagged: mean · system of equations

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