Coin banknote box

Matthew had 2 euro coins and 5 euro banknotes in his box. There were a total of 60 of them worth 171 euros. How much money did Matthew have in the treasury?

Final Answer:

a =  43
b =  17

Step-by-step explanation:

$$\begin{gathered} a+b=60 \\ 2a+5b=171 \\ 2\cdot a+5\cdot b=171 \\ a+b=60 \\ 2a+5b=171 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ -1.5b=-25.5 \\ b=\frac{-25.5}{-1.5}=17 \\ a=\frac{171-5b}{2}=\frac{171-5\cdot 17}{2}=43 \\ a=43 \\ b=17 \end{gathered}$$

Try another example