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

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==Solution== | ==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> | + | WLOG, assume there are <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> |

+ | |||

+ | ==Solution 2== | ||

+ | Let there be <math>3x</math> students in the morning class and <math>4x</math> students in the afternoon class. The total number of students is <math>3x + 4x = 7x</math>. The average is <math>\frac{3x\cdot84 + 4x\cdot70}{7x}=76</math>. Therefore, the answer is <math>\boxed{\textbf{(C)}76}</math>. | ||

+ | <br><br> | ||

+ | ~ {TSun} ~ |

## Revision as of 19:25, 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 are students in the morning class and in the afternoon class. Then the average is

## Solution 2

Let there be students in the morning class and students in the afternoon class. The total number of students is . The average is . Therefore, the answer is .

~ {TSun} ~