# Difference between revisions of "2021 AMC 12B Problems/Problem 4"

(Created page with "The 2021 AMC 12B will be held on February 10th, 2021. The problems will not be made public until 24 hours after that.") |
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− | The | + | ==Problem== |

+ | Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is <math>84</math>, and the afternoon class's mean score is <math>70</math>. The ratio of the number of students in the morning class to the number of students in the afternoon class is <math>\frac{3}{4}</math>. What is the mean of the scores of all the students? | ||

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+ | <math>\textbf{(A)} ~74 \qquad\textbf{(B)} ~75 \qquad\textbf{(C)} ~76 \qquad\textbf{(D)} ~77 \qquad\textbf{(E)} ~78</math> | ||

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+ | ==Solution== | ||

+ | WLOG assume there <math>3</math> students in the morning class and <math>4</math> in the afternoon class. Then the average is <math>\frac{3\cdot 84 + 4\cdot 70}{7}=\boxed{\textbf{(C)} ~76}</math> |

## Revision as of 18:39, 11 February 2021

## Problem

Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is , and the afternoon class's mean score is . The ratio of the number of students in the morning class to the number of students in the afternoon class is . What is the mean of the scores of all the students?

## Solution

WLOG assume there students in the morning class and in the afternoon class. Then the average is