# Men, women and children

On the trip went men, women, and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus had a revenue of 4,200 crowns?

z =  12

### Step-by-step explanation:

60d + 150m + 150z = 4200
m = 2k
z = 3k
d= 5k

60·d + 150·m + 150·z = 4200
m = 2·k
z = 3·k
d= 5·k

60d+150m+150z = 4200
2k-m = 0
3k-z = 0
d-5k = 0

Row 4 - 1/60 · Row 1 → Row 4
60d+150m+150z = 4200
2k-m = 0
3k-z = 0
-5k-2.5m-2.5z = -70

Pivot: Row 2 ↔ Row 4
60d+150m+150z = 4200
-5k-2.5m-2.5z = -70
3k-z = 0
2k-m = 0

Row 3 - 3/-5 · Row 2 → Row 3
60d+150m+150z = 4200
-5k-2.5m-2.5z = -70
-1.5m-2.5z = -42
2k-m = 0

Row 4 - 2/-5 · Row 2 → Row 4
60d+150m+150z = 4200
-5k-2.5m-2.5z = -70
-1.5m-2.5z = -42
-2m-z = -28

Pivot: Row 3 ↔ Row 4
60d+150m+150z = 4200
-5k-2.5m-2.5z = -70
-2m-z = -28
-1.5m-2.5z = -42

Row 4 - -1.5/-2 · Row 3 → Row 4
60d+150m+150z = 4200
-5k-2.5m-2.5z = -70
-2m-z = -28
-1.75z = -21

z = -21/-1.75 = 12
m = -28+z/-2 = -28+12/-2 = 8
k = -70+2.5m+2.5z/-5 = -70+2.5 · 8+2.5 · 12/-5 = 4
d = 4200-150m-150z/60 = 4200-150 · 8-150 · 12/60 = 20

d = 20
k = 4
m = 8
z = 12

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