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 =  0.9 Eur

Step-by-step explanation:

$$\begin{gathered} 2y+3x=t \\ 4y+0.50=t \\ 5y-0.60=t \\ y-0.60-0.50=0 \\ y=0.60+0.50=1.1 \\ t=4\cdot y+0.50=4\cdot 1.1+0.50=\frac{49}{10}=4.9 \\ 2\cdot y+3\cdot x=t \\ 2\cdot 1.1+3\cdot x=4.9 \\ 3x=2.7 \\ x=\frac{2.7}{3}=0.9 \\ x=\frac{9}{10}=0.9=0.9\text{Eur} \end{gathered}$$

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