2023 AMC 10A Problems/Problem 10
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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 a represent the amount of tests taken previously and x the mean of the scores taken previously. We can write the equation (ax+11)/a+1 = x+1 and (ax+33)/a+3 = x+2. Expanding, ax+11 = ax+a+x+1 and ax+33 = ax+2a+3x+6. This gives us a+x = 10 and 2a+3x = 27. Solving for each variable, x=7 and a=3. (D)
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