2023 AMC 10A Problems/Problem 10

Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an $11$ on the next quiz, her mean will increase by $1$ . If she scores an $11$ on each of the next three quizzes, her mean will increase by $2$ . What is the mean of her quiz scores currently? $\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8$

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)

~walmartbrian ~Shontai

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2023 AMC 10A Problems/Problem 10