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

Line 19: Line 19:
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2021|ab=B|num-b=3|num-a=5}}
 
{{AMC12 box|year=2021|ab=B|num-b=3|num-a=5}}
 +
{{AMC10 box|year=2021|ab=B|before=[[2021 AMC 10A]]|after=[[2022 AMC 10A]]}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 00:33, 12 February 2021

Problem

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

$\textbf{(A)} ~74 \qquad\textbf{(B)} ~75 \qquad\textbf{(C)} ~76 \qquad\textbf{(D)} ~77 \qquad\textbf{(E)} ~78$

Solution

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

Solution 2

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

~ {TSun} ~

Video Solution by OmegaLearn (Clever application of Average Formula)

https://youtu.be/lE8v7lXT8Go

~ pi_is_3.14

See Also

2021 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
2021 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
2021 AMC 10A
Followed by
2022 AMC 10A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS