Question 1182878
-Adam, Bipin and Chen together scored 200 marks.<pre>A+B+C = 200</pre>-Bipin, Chen and Dana together scored 215 marks.<pre>B+C+D = 215</pre>-Chen, Dana and Erica together scored 224 marks.<pre>C+D+E = 224</pre>-The two girls (Dana and Erica) scored more than Chen.<pre>D > C and E > C</pre>-The five of them together scored 350 marks<pre> A+B+C+D+E=350

So we have this system of 4 equations in 5 unknowns,
which is "under-determined":

A+B+C     = 200
  B+C+D   = 215
    C+D+E = 224
A+B+C+D+E = 350

We can reduce it to a 3x3 system by letting 
A+B=F and D+E=G in the 1st, 3rd, and 4th equations. 
Then we have this 3x3 system:

F+C   = 200
  C+G = 224
F+C+G = 350

Subtracting the 1st eq. from the 3rd gives G = 150 
Subtracting the 2nd eq. from the 3rd gives F = 126
Substitution of 126 for F in the 1st gives C = 74

So A+B = 126, D+E = 150, and C = 74.

Since we know that D and E are both greater than C=74,
let m be how much greater D is than C=74, and
let n be how much greater E is than C=74. then

D = 74+m
E = 74+n, where m and n are positive integers.

Substituting in

             D+E = 150
   (74+m)+(74+n) = 150
       74+m+74+n = 150
         148+m+n = 150
             m+n = 2

The only positive integer solution to that is

         m = 1 and n = 1.

 So D = 74+m = 74+1 = 75
And E = 74+n = 74+1 = 75

We find B from B+C+D = 215

B+74+75 = 215
  B+149 = 215
      B = 66

We find A from A+B = 126

A+66 = 126
   A = 60

So (A,B,C,D,E) = (60,66,74,75,75)

Edwin</pre>