Difference between revisions of "2023 AMC 10A Problems/Problem 10"
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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> | <math>\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8</math> | ||
| − | Solution 1 | + | ==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) | 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 | ~walmartbrian ~Shontai | ||
Revision as of 17:59, 9 November 2023
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)
~walmartbrian ~Shontai
