SOLUTION: Average score of 120 students in a test is 35 (out of 50). The average scores of students who have passed is 35, the avearage for those who failed is 15 points. Find the number of

Question 883711: Average score of 120 students in a test is 35 (out of 50). The average scores of students who have passed is 35, the avearage for those who failed is 15 points. Find the number of students who passed?
Answer by SmithWillSuffice(4) (Show Source): You can put this solution on YOUR website!
I had a version of this in my textbook, so I made the numbers the same and have pasted an image of the pages of solution attached below. (If it cannot be seen, here is the solution in brief):
You set up four simultaneous equations in the unknowns, X, Y, Nx, Ny, where
= sum of all points scored by all those who passed, X=summ of all points scored by all those who failed, Nx=number who failed, Ny=number who passed.
(1)
(2)
(3)
(4)
You can practise the algebra, or use Maxima,
(%i1) solve([Ny+Nx=120,35=(X+Y)/120,39=Y/Ny,15=X/Nx],[Ny,Nx,X,Y]);
(%o1) [[Ny = 100, Nx = 20, X = 300, Y = 3900]]
Here's the LaTeX:

.
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