Clothes

CZK 2,400 cost clothes, a sweater by 150% more than a T-shirt, trousers 2x more than a sweater, a jacket as a sweater and trousers. What did the individual clothes cost?

b =  1125
n =  750
s =  375
t =  150

Step-by-step explanation:

2400 = s+t+n+b
s = t + 1.50t
n = 2s
b=s+n

2400 = s+t+n+b
s = t + 1.50·t
n = 2·s
b=s+n

b+n+s+t = 2400
s-2.5t = 0
n-2s = 0
b-n-s = 0

Row 4 - Row 1 → Row 4
b+n+s+t = 2400
s-2.5t = 0
n-2s = 0
-2n-2s-t = -2400

Pivot: Row 2 ↔ Row 4
b+n+s+t = 2400
-2n-2s-t = -2400
n-2s = 0
s-2.5t = 0

Row 3 - 1/-2 · Row 2 → Row 3
b+n+s+t = 2400
-2n-2s-t = -2400
-3s-0.5t = -1200
s-2.5t = 0

Row 4 - 1/-3 · Row 3 → Row 4
b+n+s+t = 2400
-2n-2s-t = -2400
-3s-0.5t = -1200
-2.6667t = -400

t = -400/-2.66666667 = 150
s = -1200+0.5t/-3 = -1200+0.5 · 150/-3 = 375
n = -2400+2s+t/-2 = -2400+2 · 375+150/-2 = 750
b = 2400-n-s-t = 2400-750-375-150 = 1125

b = 1125
n = 750
s = 375
t = 150

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