Question: Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself. Each guest got $1 back: so now each guest only paid $9; bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?
Hint: Make a list of all of the people involved and how much money they ended up with/spent.
Answer: The $9 paid by each guest accounts for the $2 that went to the bellhop. So rather than adding $27 to the $2 kept by the bellhop, the $27 accounts for the bellhops money. The $27 plus the $3 kept by the guests does add up to $30.
Question: Hard, Harder, and Hardest are brothers. By age from youngest to oldest, it goes Hard, Harder, Hardest. Hard is half the age of Hardest who is 20 which means hard is 10. Harder has a two-year difference between the number of years older he is than Hard and the number of years younger he is than Hardest. Harder is closer to the age of Hard than Hardest. How old is Harder?