Tour participant calculation

Forty-eight people took part in the tour. Among them were men, women, and children. There were four more women than men and six fewer children than half of the adults. How many men, women, and children took part in the tour?

Final Answer:

d =  12
m =  16
z =  20

Step-by-step explanation:


m+z+d=48
z=4+m
d = (m+z)/2-6

d+m+z = 48
m-z = -4
2d-m-z = -12

Pivot: Row 1 ↔ Row 3
2d-m-z = -12
m-z = -4
d+m+z = 48

Row 3 - 1/2 · Row 1 → Row 3
2d-m-z = -12
m-z = -4
1.5m+1.5z = 54

Pivot: Row 2 ↔ Row 3
2d-m-z = -12
1.5m+1.5z = 54
m-z = -4

Row 3 - 1/1.5 · Row 2 → Row 3
2d-m-z = -12
1.5m+1.5z = 54
-2z = -40


z = -40/-2 = 20
m = 54-1.5z/1.5 = 54-1.5 · 20/1.5 = 16
d = -12+m+z/2 = -12+16+20/2 = 12

d = 12
m = 16
z = 20

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