# Something 5385

Janko got pocket money and wants to buy something good for it. If he purchased four cakes, it would increase by 0.50 euros. If he wanted to buy five cakes, he would miss 0.60 euros. He would spend all his pockets on the rest if he bought two cakes and three cones. 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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