Contestants

In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestants who did not get any points. Calculate the number of contestants if the average result achieved in the competition was actually 2 points.

Correct result:

n =  85

Solution:

n = 5+10+x+x
5•5+4•10+3x+0x=2n

n = 5+10+x+x
5•5+4•10+3•x+0•x=2•n

n-2x = 15
2n-3x = 65

n = 85
x = 35

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