Dostaneli

If we get 5% of the amount that Petr has in his wallet and 4% of the amount that Paul has with him, we will have 46 CZK. However, if we get 4% from Peter's and 5% from Paul's, we will only have 44 CZK. How many crowns do Petr and Paul have with them?
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Correct answer:

a =  600 Kc
b =  400 Kc

Step-by-step explanation:

$$\begin{gathered} 0.05a+0.04b=46 \\ 0.04a+0.05b=44 \\ 0.05\cdot a+0.04\cdot b=46 \\ 0.04\cdot a+0.05\cdot b=44 \\ 0.05a+0.04b=46 \\ 0.04a+0.05b=44 \\ Row2-\frac{0.04}{0.05}\cdot Row1\to Row2 \\ 0.05a+0.04b=46 \\ 0.02b=7.2 \\ b=\frac{7.2}{0.018}=400 \\ a=\frac{46-0.039999999999999b}{0.05}=\frac{46-0.04\cdot 400}{0.05}=600=600\text{Kc} \\ a=600 \\ b=400 \end{gathered}$$

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