Does Maths make you feel like a fool?
As it’s April Fool’s Day, here’s a puzzle that causes some bother for many people. (It’s copied from an American blog, hence the $ signs)
There are 3 traveling salesmen, traveling together to a convention. It is late at night and they are very tired and decide to stop at a country inn for a few hours sleep. The inn only has one room left with a double bed and an couch. salesmen are tired and take the room as a few hours sleep is all they want. The room is $30.00, each of the 3 contribute $10.00.
In the morning the manager of the inn arrives. He feels bad about the uncomfortable room provided these 3 men and hoping to attract them back again decides to give them a partial refund. He gives the bell boy $5.00 to take to the room and give to these salesmen.
The bell boy realizes the men are not expecting any sort of refund. So he decides to give them back only $3.00 and keeps $2.00 for himself.
He gives the 3 men the $3.00 refund, each man takes a dollar. So as each of the men had originally paid $10.00, but as each had received a dollar back. It ended up costing each man $9.00. They are happy with this and the bell boy is happy as he has $2.00 in his pocket.
Question: each of the 3 men ended up paying $9.00. 3X9=27+2(money in bellboys pocket)=29. We started with $30.00 what has happened to the extra $1.00. All my numbers are correct, why doesn’t this math work?
Sometimes, Maths makes people feel like fools. As teachers we need to be able to help children break down problems. Why has the man got himself into this dilemma? What is he doing wrong? In fact, is he doing anything wrong at all. He receives his answer from another blogger who says that sometimes maths can be like a magician’s sleight of hand. The information looks like it’s true but you’ve been bamboozled! Here’s her response:
This is a mathematical sleight-of-hand problem. You know how a stage magician waves one hand while talking fast, so that you fail to notice what he is doing with the other hand. In the same way, the writer of this problem waves numbers around without meaning. The individual numbers are not difficult, but the barrage of them distracts the reader so that you fail to notice what has really happened.
Each man pays a net $9 for the room. Total payment = 3x$9 =$27.
The manager gets $25 = the original $30 payment, minus a $5 refund.
The bellboy takes for himself a tip of $2.
True equation: 3 x 9 = 25 + 2. What was paid equals what was received.
The source of this Maths problem is: http://letsplaymath.net/2007/08/17/pre-algebra-problem-solving-the-tools/#comment-6029