Society people distribution

There are men, women, and children in society. There are 3 times more men than women and 5 more children than women. If 6 more men and 6 women came, men would be half the company. How many women, men, and children are there?

Final Answer:

d =  10
m =  15
z =  5

Step-by-step explanation:


m=3z
d = 5+z
6+m = (m+6+z+6+d)/2

m=3·z
d = 5+z
6+m = (m+6+z+6+d)/2

m-3z = 0
d-z = 5
d-m+z = 0

Pivot: Row 1 ↔ Row 2
d-z = 5
m-3z = 0
d-m+z = 0

Row 3 - Row 1 → Row 3
d-z = 5
m-3z = 0
-m+2z = -5

Row 3 + Row 2 → Row 3
d-z = 5
m-3z = 0
-z = -5


z = -5/-1 = 5
m = 0+3z = 0+3 · 5 = 15
d = 5+z = 5+5 = 10

d = 10
m = 15
z = 5

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