# A Bargain Hotel?

## Math Puzzles of the Month A Bargain Hotel?

Diego Reyes submitted this month's puzzle.

Three Schlumberger employees, after a day of work in a remote location, arrived at a hotel to pass the night. They approached the concierge and asked for three rooms. The concierge gave them the three rooms at \$10 per room. Each Schlumberger mate paid \$10 (\$30 in total) and went to sleep.

Later the concierge approached the hotel manager and told her about the guests who had just arrived. The manager reminded the concierge that the hotel had a special rate for Schlumberger employees and he should charge only \$25 in total for the three rooms.

The next morning when the guests were checking out, the concierge remembered the change in rate and returned five dollar bills to the employees; each one of them took \$1, and they left \$2 as a tip for the concierge.

### Summarizing

• Each employee paid \$10.
• Each employee received \$1 as a refund, so in the end, each one paid only \$9.
• In total they paid \$27; that is, 3 times \$9.
• Adding the \$2 tip, the total is \$29

But the Schlumberger employees paid \$30 in total, so where’s the missing dollar?

After you've tried this for yourself, check our solution.