Question

Three friends are on a road trip, and they rent a triple room for a night. When they get to the hotel, they pay the fee of $30 and go up to their room. The porter brings up their bags and refunds them $5 because the hotel is running a weeknight special. The three friends each keep one of the dollars and give the porter a $2 tip. Later, they sit down to work out their expenses for the weekend and find they have a problem.

They each paid $10 for the room and got $1 back each, making their contributions $9. Then they gave the porter a $2 tip. However, 9 times three is 27, plus two is $29. Where did the extra dollar go?

Answer 1

The error in the calculation is in adding up the wrong numbers. The three friends paid a total of $27 for the room ($9 each) and gave the porter a $2 tip, making the total expenses $29. The extra dollar is not missing, but it was never part of the expenses in the first place. The mistake arises from adding up the $27 they paid for the room with the $2 tip they gave the porter, which gives $29. However, this sum includes the $3 they got back from the hotel, which should not be included in the expenses since they received it back.

Another way to think about it is to subtract the $3 they got back from the $30 they paid initially. This gives $27, which is the amount they actually spent on the room. Then, when they added the $2 tip for the porter, the total expenses for the weekend were $29, as expected.

So, the mistake is not in the missing dollar, but in adding up the wrong numbers.