Pocket money

John receives pocket money and wants to buy some treats. If he bought four cakes, he would have CZK 5 left. If he wanted to buy five cakes, he would be CZK 6 short. If he bought two pies and three doughnuts, he would spend all his pocket money with nothing left over. How much does one doughnut cost?

Final 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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