Banknotes

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

Correct result:

n =  3

Solution:

310=50a+20b 310=2⋅5⋅31 50=2⋅52 20=22⋅5 GCD(310,50,20)=2⋅5=10  d=GCD(310,50,20)=10  31=5a+2b  a1=1,b1=13 a2=3,b2=8 a3=5,b3=3  n=3

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