The treasury

Lucy has only two-crown and five-crown coins in her treasury. She has 30 coins worth 108 Czech crowns (CZK). How many two-crown and how many five-crown coins does she have?

Correct answer:

a =  14
b =  16

Step-by-step explanation:

$$\begin{gathered} 30=a+b \\ 108=2a+5b \\ 30=a+b \\ 108=2\cdot a+5\cdot b \\ a+b=30 \\ 2a+5b=108 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a+5b=108 \\ a+b=30 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+5b=108 \\ -1.5b=-24 \\ b=\frac{-24}{-1.5}=16 \\ a=\frac{108-5b}{2}=\frac{108-5\cdot 16}{2}=14 \\ a=14 \\ b=16 \end{gathered}$$

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