1952 AHSME Problems/Problem 2

Revision as of 17:51, 1 January 2014 by Throwaway1489 (talk | contribs) (Created page with "== Problem== Two high school classes took the same test. One class of <math> 20 </math> students made an average grade of <math> 80\% </math>; the other class of <math> 30 </mat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Two high school classes took the same test. One class of $20$ students made an average grade of $80\%$; the other class of $30$ students made an average grade of $70\%$. The average grade for all students in both classes is:

$\textbf{(A)}\ 75\%\qquad \textbf{(B)}\ 74\%\qquad \textbf{(C)}\ 72\%\qquad \textbf{(D)}\ 77\%\qquad \textbf{(E)\ }\text{none of these}$

Solution

The desired average can be found by dividing the total number of points earned by the total number of students. There are $20\cdot 80+30\cdot 70=3700$ points earned and $20+30=50$ students. Thus, our answer is $\frac{3700}{50}$, or $\boxed{\textbf{(B)}\ 74\%}$.

See also

1952 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

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