December 16, 2011

THE MISSING COIN PROBLEM

© Ben Heine
Have you ever encountered the problem regarding the missing coin? Here it is:

A man wanted to buy a book worth 97 pesos but he does not have money for it. He decided to borrow from his friends. He borrowed 50 pesos each from his two friends. Now he has 100 pesos, which is enough to buy the book. He then bought the book and got a change of 3 pesos.

Since he still have 3 pesos, he decided to pay 1 peso each to his friends. He then only have 49 pesos credit from each of his friends.

The question is that, since he has 49 pesos credit for each friend and one peso at hand, that is
  49 + 49 = 98   (credit from his friend
  98 + 1 = 99     (the 1 peso is available at hand)

The total is 99 pesos but the original amount is 100 pesos. Where is the other one peso?

Post your answers here with your explanations...

© Ben Heine
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Note: All images used are with the permission of the owner, Mr. Ben Heine, a Belgian visual artist. You can visit his website and page at

http://www.benheine.com/
http://www.facebook.com/pages/Ben-Heine/45292293615 

5 comments:

Initially, your credit is equal to your money on hand:

97 + 1 + 1 + 1 = 50 + 50

Since, you pay your lenders 2-peso coins, we'll transpose 2-peso coins to the other side of equation (which is your debt):

97 + 1 = 50 + 50 - 1 - 1

Simplified:

98 = 98

Sensya na Sir ah, di ko masyado alam mga terminologies sa Math, tama ba yung transposition?

97 was the amount to be paid.
Divide 97 by 2 and you'll get 48.5 .
48.5 was the only needed price to be borrowed from each of his 2 friends.
Since he got a change of 3 and he's returning 1.5 to each and he owes his 2 friends 48.5 each.

48.5 + 1.5 = 50 x 2 = 100

*Sometimes, we have to analyze the problem first. Some details were made just to confuse the readers.....Hope you understand it!

97 / 2 = 48.5
3 / 2 = 1.5
48.5 + 1.5 = 50 x 2 = 100

EASY!

don't add the remaining 1 peso. subtract it from 98. It balances with 97-peso book.

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