Pocket money

Charles spent half of his pocket money. He gave two-thirds of the rest to his friend Michael. He had 50 CZK left from his pocket money.

A. Calculate how much money Charles gave Michael.

B. Calculate how much money Charles received as pocket money.

Final Answer:

M =  100 Kc
K =  300 Kc

Step-by-step explanation:

$$\begin{gathered} K-K/2-M=50 \\ K-K/2-\frac{2}{3}\cdot (K-K/2)=50 \\ K-\frac{K}{2}-\frac{2}{3}\cdot (K-\frac{K}{2})=50 \\ K-K/2-2/3\cdot (K-K/2)=50 \\ K=300 \\ M=\frac{2}{3}\cdot (K-K/2)=\frac{2}{3}\cdot (300-300/2)=100\text{Kc} \end{gathered}$$

$$\begin{gathered} K=300=300\text{Kc} \\ \text{ Verifying Solution: } \\ {k}_1=K=300\text{Kc} \\ {k}_2=K-K/2=300-300/2=150\text{Kc} \\ {m}_2=\frac{2}{3}\cdot k_2=\frac{2}{3}\cdot 150=\frac{2\cdot 150}{3}=\frac{300}{3}=100\text{Kc} \\ {k}_3=k_2-m_2=150-100=50\text{Kc} \end{gathered}$$

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