Contestants

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

Correct answer:

n =  85

Step-by-step explanation:

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

Pivot: Row 1 ↔ Row 2
2n-3x = 65
n-2x = 15

Row 2 - 1/2 · Row 1 → Row 2
2n-3x = 65
-0.5x = -17.5


x = -17.5/-0.5 = 35
n = 65+3x/2 = 65+3 · 35/2 = 85

n = 85
x = 35

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