Banknotes 83131

Cashier Samuel had a total of 20 banknotes in the cash register with a total value of 850 euros. They were only €50 and €20 notes. How many of each bill did he have?

Correct answer:

a =  15
b =  5

Step-by-step explanation:

$$\begin{gathered} a+b=20 \\ 50a+20b=850 \\ a+b=20 \\ 50\cdot a+20\cdot b=850 \\ a+b=20 \\ 50a+20b=850 \\ Pivot:Row1\leftrightarrow Row2 \\ 50a+20b=850 \\ a+b=20 \\ Row2-\frac{1}{50}\cdot Row1\to Row2 \\ 50a+20b=850 \\ 0.6b=3 \\ b=\frac{3}{0.6}=5 \\ a=\frac{850-20b}{50}=\frac{850-20\cdot 5}{50}=15 \\ a=15 \\ b=5 \end{gathered}$$

Try another example