Pocket money

Karol 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 Karol gave Michael.

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

Final Answer:

M =  100 Kc
K =  300 Kc

Step-by-step explanation:

$$\begin{gathered} K-K/2-M=50 \\ K-K/2-\frac{2}{3}\cdot (K-K/2)=50 \\ K-\frac{K}{2}-\frac{2}{3}\cdot (K-\frac{K}{2})=50 \\ K-K/2-2/3\cdot (K-K/2)=50 \\ K=300 \\ K=\frac{300}{1}=300 \\ K=300 \\ M=\frac{2}{3}\cdot (K-K/2)=\frac{2}{3}\cdot (300-300/2)=100\text{Kc} \end{gathered}$$

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

Try another example