Audience 3369

In the hockey audience between Sweden and Finland, there are 126 men, 65 boys, 46 children from Sweden, 50 children from Finland, and 200 Swedes, of which half are men and 39 women from Finland. How many people are in the audience?

Correct answer:

n = 361

Step-by-step explanation:

126 = s+f
200 = f+x
f = x
z = 39+x
n=126+z+46+50

f+s = 126
f+x = 200
f-x = 0
x-z = -39
n-z = 222

Row 2 - Row 1 → Row 2
f+s = 126
-s+x = 74
f-x = 0
x-z = -39
n-z = 222

Row 3 - Row 1 → Row 3
f+s = 126
-s+x = 74
-s-x = -126
x-z = -39
n-z = 222

Pivot: Row 2 ↔ Row 5
f+s = 126
n-z = 222
-s-x = -126
x-z = -39
-s+x = 74

Row 5 - Row 3 → Row 5
f+s = 126
n-z = 222
-s-x = -126
x-z = -39
2x = 200

Pivot: Row 4 ↔ Row 5
f+s = 126
n-z = 222
-s-x = -126
2x = 200
x-z = -39

Row 5 - 1/2 · Row 4 → Row 5
f+s = 126
n-z = 222
-s-x = -126
2x = 200
-z = -139

z = -139/-1 = 139
x = 200/2 = 100
s = -126+x/-1 = -126+100/-1 = 26
n = 222+z = 222+139 = 361
f = 126-s = 126-26 = 100

f = 100
n = 361
s = 26
x = 100
z = 139

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