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The three friends divided the money earned as follows: Tonda got 2/5, Karel 2/9, and Jirko took the rest of CZK 102. How much did each of them earn?

Correct answer:

t =  108 Kc
k =  60 Kc

Step-by-step explanation:

$$\begin{gathered} j=102\text{Kc} \\ T=\frac{2}{5}=0.4 \\ K=\frac{2}{9}\doteq 0.2222 \\ J=1-T-K=1-\frac{2}{5}-\frac{2}{9}=\frac{17}{45}\doteq 0.3778 \\ J\cdot x=j \\ x=j/J=102/\frac{17}{45}=102:\frac{17}{45}=102\cdot \frac{45}{17}=\frac{102\cdot 45}{17}=\frac{4590}{17}=270\text{Kc} \\ t=T\cdot x=\frac{2}{5}\cdot 270=\frac{2\cdot 270}{5}=\frac{540}{5}=108\text{Kc} \end{gathered}$$

$k=K\cdot x=\frac{2}{9}\cdot 270=\frac{2\cdot 270}{9}=\frac{540}{9}=60\text{Kc}$

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