# Something 5385

Janko got a pocket money and wants to buy something good for it. If he bought four cakes, it would increase 0.50 e. If he wanted to buy 5 cakes, he would miss 0.60 e. If he bought two cakes and three cones, he would spend all his pockets on the rest. How much does one pine cone cost?

s =  0.9 Eur

### Step-by-step explanation:

4k + 0.50 = v
5k = v + 0.60
2k+3s = v

4·k + 0.50 = v
5·k = v + 0.60
2·k+3·s = v

4k-v = -0.5
5k-v = 0.6
2k+3s-v = 0

Pivot: Row 1 ↔ Row 2
5k-v = 0.6
4k-v = -0.5
2k+3s-v = 0

Row 2 - 4/5 · Row 1 → Row 2
5k-v = 0.6
-0.2v = -0.98
2k+3s-v = 0

Row 3 - 2/5 · Row 1 → Row 3
5k-v = 0.6
-0.2v = -0.98
3s-0.6v = -0.24

Pivot: Row 2 ↔ Row 3
5k-v = 0.6
3s-0.6v = -0.24
-0.2v = -0.98

v = -0.98/-0.2 = 4.9
s = -0.24+0.6v/3 = -0.24+0.6 · 4.9/3 = 0.9
k = 0.6+v/5 = 0.6+4.9/5 = 1.1

k = 11/10 = 1.1
s = 9/10 = 0.9
v = 49/10 = 4.9

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