The Missing Buck

      A team of three junior high school boys received a twenty-dollar prize for winning a science contest at the Anniversary Day festival. They decided to purchase a soccer ball for 15 dollars and got 5 dollars for change. Since it had been difficult to have the 5-dollar change divisible for the three of them, they agreed to contribute 2 dollars to a local orphanage. So they went home with each one of them getting a one-dollar share.

      Upon getting home, one of the boys was somewhat curious to recalculate their detailed expenses out of the total amount of 20 dollars.

      He then began with his calculation as follows:
- The soccer ball that they bought together cost 15 dollars.
- He assumed that each one of them shared 5 dollars to pay.
- But since they had brought back home a dollar each, he also assumed that they had spent altogether an amount of only 12 dollars, i.e. a 4-dollar spending for each one of them.

      He made a resume for his calculation as follows:
- Purchase of the soccer ball had only cost them 12 dollars.
- Change they received from purchasing the ball, 5 dollars.
- Contributed to the orphanage,                          2 dollars.
- So, the total expense was only                       19 dollars.
Then what has happened to the "seemingly missing" one buck?

      Try to help the boy solve the problem, but please do not take things easy by just reading directly the solution below.

A Suggested Solution:
      Within the amount of the 5-dollar change, already included the 2 dollars contributed to the orphanage. So, this amount might not be calculated as a separate spending any more. In other words, the 2 dollars should not be added to the 5 dollars because it had been already a part of it.
      This was the main reason that seemed to cause such an incorrect calculation (by the boy).
      Therefore, the correct calculation should rather comply with the following:
- Purchase of soccer ball would remain                 15 dollars
- While spending of the 5-dollar change should
   rather be listed as follows:
    - Contributed to the orphanage,                        2 dollars
    - Distributed to the three boys (a dollar each),   3 dollars
- The total expenses would then remain               20 dollars

      Well, not a single penny was missing!