Something 5588

Honza receives pocket money and wants to buy something good with it. If he purchased four cakes, he would have CZK 5 left. If he wanted to buy five cakes, he would be 6 CZK short. If he had bought two pies and three doughnuts, he would have spent all his pocket money with nothing left over. How much does one donut cost?

Correct answer:

x =  9 Kc

Step-by-step explanation:


2y+3x = t
4y + 5 = t
5y - 6 = t

2·y+3·x = t
4·y + 5 = t
5·y - 6 = t

t-3x-2y = 0
t-4y = 5
t-5y = -6

Row 2 - Row 1 → Row 2
t-3x-2y = 0
3x-2y = 5
t-5y = -6

Row 3 - Row 1 → Row 3
t-3x-2y = 0
3x-2y = 5
3x-3y = -6

Row 3 - Row 2 → Row 3
t-3x-2y = 0
3x-2y = 5
-y = -11


y = -11/-1 = 11
x = 5+2y/3 = 5+2 · 11/3 = 9
t = 0+3x+2y = 0+3 · 9+2 · 11 = 49

t = 49
x = 9
y = 11

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