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> |
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| + | ==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 18:25, 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} ~
