Saleswoman 2667

Martin bought goods in the store for 260 CZK. He paid with a thousand CZK crowns. The saleswoman returned 18 banknotes and coins worth CZK 10 and CZK 50. How many of each value were there?

Correct answer:

a =  4
b =  14

Step-by-step explanation:

$$\begin{gathered} a+b=18 \\ 10a+50b=1000-260 \\ a+b=18 \\ 10\cdot a+50\cdot b=1000-260 \\ a+b=18 \\ 10a+50b=740 \\ Pivot:Row1\leftrightarrow Row2 \\ 10a+50b=740 \\ a+b=18 \\ Row2-\frac{1}{10}\cdot Row1\to Row2 \\ 10a+50b=740 \\ -4b=-56 \\ b=\frac{-56}{-4}=14 \\ a=\frac{740-50b}{10}=\frac{740-50\cdot 14}{10}=4 \\ a=4 \\ b=14 \end{gathered}$$

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