The Missing Dollar Riddle

Desy showed me this problem that she had encountered on an Internet post and asked for my thoughts:

This is a variation on the famous Missing Dollar Riddle described in Wikipedia as having a long history. It's not immediately apparent why the amounts in the two columns should differ. However, first the translation of the Indonesian into English. 

A boy has 50,000 rupiah. He buys some bread for 20,000 rupiah and thus has 30,000 left. He buys some juice for 15,000 and has 15,000 left. He buys a drink for 9,000 and has 6,000 left. Finally, he spends his remaining 6,000 rupiah on cake and has no money left. The question asked is why is there a difference of 1,000 rupiah. What is the answer to this question?

In attempting to answer the question, I thought I'd look at what happens when the amounts spent are different to those shown above. Firstly though, let's get rid of the 1000's and work with 20, 15, 9 and 6. Suppose the boy spent 20.5, 15.5, 8.5 and 5.5 instead. The progressive amounts left at each stage are 29.5, 14.0, 5.5 and 0, totalling 49. In this case, the progressive totals underestimate by 1 instead of overestimating by 1. I then considered the case where the boy spends 20.25, 15.25, 8.75 and 5.75. The corresponding amounts left are 29.75, 14.5, 5.75 and 0. These total 50 and so there is no difference.

The conclusion is that the progressive totals for the amount of money left are sometimes in excess of the amount of money spent, sometimes less than it and sometimes equal to it. Clearly the progressive totals are measuring something that's close to the amount of money spent but generally not the same as it. At this point, I turned to algebra to explore the generality of what is really going on.

To do this consider the initial amount of money are being M and the amounts spent are a, b, c and d. Because all the money is spent, we can say that d=M-a-b-c and so the amounts spent are a, b, c and M-a-b-c. The progressive amounts of money left are then M-a, M-a-b, M-a-b-c and 0. These amounts total 3M-3a-2b-c and clearly do not necessarily equal M.

However, what happens when they do? What happens if 3M-3a-2b-c = M? In this case, we get 2M = 3a+2b+c. For the particular case referred to above, M=50 and so 2M=100. For the case where a=29.75, b=14.5 and c=5.75, it can be seen that 3a+2b+c = 60.75+30.50+8.75 = 100 and so the equation is satisfied. There are many values of a, b and c that satisfy the equation. For example, a=20, b=15 and c=10 but a=20, b=15 and c=9 (the problem as it appeared in the Instagram post above) does not.