Banknotes

How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.

Correct answer:

n =  3

Step-by-step explanation:

$$\begin{gathered} 310=50a+20b \\ 310=2\cdot 5\cdot 31 \\ 50=2\cdot 5^2 \\ 20=2^2\cdot 5 \\ \text{GCD}(310,50,20)=2\cdot 5=10 \\ d=GCD(310,50,20)=10 \\ 31=5a+2b \\ {a}_1=1,b_1=13 \\ {a}_2=3,b_2=8 \\ {a}_3=5,b_3=3 \\ n=3 \end{gathered}$$

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