Groschens

The young journeyman bought a cloak, hat, and galoshes. He paid 200 grosz for everything. A cloak costs 90 groschen, more than a hat, and a hat with a cape costs 160 groschen, more than a galoshes. How much groschen did the cloak cost, and how many hats and galoshes?

Correct answer:

g =  20
k =  45
p =  135

Step-by-step explanation:


p+k+g=200
p=90+k
k+p=160+g

g+k+p = 200
k-p = -90
g-k-p = -160

Row 3 - Row 1 → Row 3
g+k+p = 200
k-p = -90
-2k-2p = -360

Pivot: Row 2 ↔ Row 3
g+k+p = 200
-2k-2p = -360
k-p = -90

Row 3 - 1/-2 · Row 2 → Row 3
g+k+p = 200
-2k-2p = -360
-2p = -270


p = -270/-2 = 135
k = -360+2p/-2 = -360+2 · 135/-2 = 45
g = 200-k-p = 200-45-135 = 20

g = 20
k = 45
p = 135

Our linear equations calculator calculates it.



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