Suppose an ATM can only provide 20 and 50 notes and allows t

Suppose an ATM can only provide $20 and $50 notes and allows the user to choose the way in which the cash is obtained: for example. $140 may be obtained as 2 Times $50 and 2 Times $20 or as 7 Times $20. Find all solutions of the linear Diophantine equation 50x + 20y = 480 x, y Z. Determine the number of ways that a user can withdraw $480. Find the solution with the least amount of $20 notes. How many of each note is required? Would a user withdraw $365 from the ATM? Why or why not?

Solution

a)x cannot be odd as then y will be fraction

   (0,24), (2,19), (4,14), (6,9), (8,4)

b)5 ways

c)$20 notes = 4

   $50 notes = 8

d)no, since $20 and $50 are not a factor of $365.