Forty-eight 24101

Forty-eight people were present at the reception. Among them were Czechs, Slovaks, and Germans. Slovaks were 4 more than Czechs and Germans 6 less than half Czechs and Slovaks. How many Czechs, Slovaks, and Germans were there at the reception?

Correct answer:

c =  16
n =  12
s =  20

Step-by-step explanation:


c+s+n=48
s=4+c
n=(c+s)/2-6

c+n+s = 48
c-s = -4
c-2n+s = 12

Row 2 - Row 1 → Row 2
c+n+s = 48
-n-2s = -52
c-2n+s = 12

Row 3 - Row 1 → Row 3
c+n+s = 48
-n-2s = -52
-3n = -36

Pivot: Row 2 ↔ Row 3
c+n+s = 48
-3n = -36
-n-2s = -52

Row 3 - -1/-3 · Row 2 → Row 3
c+n+s = 48
-3n = -36
-2s = -40


s = -40/-2 = 20
n = -36/-3 = 12
c = 48-n-s = 48-12-20 = 16

c = 16
n = 12
s = 20

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