Four-times of an age

Karel's age is two-fifths the age of his older brother Michal. Two years ago, Karel was four times younger than Michal. How old is Karel now?

Correct answer:

k =  4

Step-by-step explanation:

$$\begin{gathered} \frac{2}{5}\cdot m=k \\ 4\cdot (k-2)=m-2 \\ 2/5\cdot m=k \\ 4\cdot (k-2)=m-2 \\ 5k-2m=0 \\ 4k-m=6 \\ Row2-\frac{4}{5}\cdot Row1\to Row2 \\ 5k-2m=0 \\ 0.6m=6 \\ m=\frac{6}{0.6}=10 \\ k=\frac{0+2m}{5}=\frac{0+2\cdot 10}{5}=4 \\ k=4 \\ m=10 \end{gathered}$$

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