Two-thirds 82565

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

A. Calculate how much money Karol gave Michal.

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

Correct answer:

M =  100 Kc
K =  300 Kc

Step-by-step explanation:

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

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

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