Cactus violet sales

At the flower festival, young growers sold cactus plants for CZK 12 and indoor violet plants for CZK 9. They sold a total of 47 pieces of flowers of both types and received CZK 501. How many cacti and how many violets did they sell?

Final Answer:

k =  26
f =  21

Step-by-step explanation:

$$\begin{gathered} k+f=47 \\ 12k+9f=501 \\ 12\cdot k+9\cdot f=501 \\ f+k=47 \\ 9f+12k=501 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{9}\cdot Row1\to Row2 \\ -0.33k=-8.67 \\ k=\frac{-8.66666667}{-0.33333333}=26 \\ f=\frac{501-12k}{9}=\frac{501-12\cdot 26}{9}=21 \\ f=21 \\ k=26 \end{gathered}$$

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