# Can You Solve This Math Riddle?

By Eowyn @DrEowyn

Three women friends went on a vacation in the Caribbean. To save money, they would share a hotel room.

The daily rate for the hotel room is \$300.

Each woman paid \$100, making up the \$300. But the hotel manager decided to give the women a discount and charged only \$250 for the room. He told a clerk to return \$50 to the three women. The clerk pocketed \$20 for himself, and gave the remaining \$30 back to the three women.

Each woman got \$10 back. Therefore, each woman actually paid \$90 (100-10) to the hotel.

\$90 x 3 = \$270

\$270 + the clerk’s \$20 = \$290

But the women originally gave the hotel \$300.

## Stumped?

Scroll down for the solution!

You’re stumped because you’ve been misled by how the question was posed to you.

Instead of looking at it as the three ladies actually paying \$270, plus the \$20 pocketed by the hotel clerk, thus equaling \$290, which means \$10 are uncounted for, the correct way to look at it is to start with the facts that we’ve been told:

• Fact #1: Each woman initially paid \$100 each.
• Fact #2: Each woman got \$10 back.
• That means each woman actually paid \$90 each.
• In other words, altogether the women paid the hotel \$270, not \$300.
• Fact #3: The hotel only charged them for and kept \$250.
• Fact #4: The hotel clerk stole \$20.
• \$20 + \$250 = \$270.
• There never was any “remaining \$10″!

Another way to look at it is to look at what happened to the \$300 that the 3 women originally paid the hotel:

• Hotel kept \$250.
• Clerk stole \$20.
• Women got \$30 back.
• 250+20+30 = \$300.
• Once again, there’s no “remaining \$10″!

~Eowyn