Coin savings calculation

Jane saves two-crown and five-crown coins. She has ten coins in the piggy bank. How many are two-crown coins and how many are five-crown coins if she has saved CZK 29?

Final Answer:

a =  7
b =  3

Step-by-step explanation:

$$\begin{gathered} a+b=10 \\ 2a+5b=29 \\ 2\cdot a+5\cdot b=29 \\ a+b=10 \\ 2a+5b=29 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ -1.5b=-4.5 \\ b=\frac{-4.5}{-1.5}=3 \\ a=\frac{29-5b}{2}=\frac{29-5\cdot 3}{2}=7 \\ a=7 \\ b=3 \end{gathered}$$

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