5. The Hotel Bill Three sales representatives attending a convention decided to

Question

5. The Hotel Bill Three sales representatives attending a convention decided to share a room in order to take advantage of some cheaper hotel rates. The clerk at the desk charged them $60, which they paid with cash. A little while later, the clerk discovered that he had made an error; the room should have only been $55. He dispatched a bellhop and returned S1 to each of the women. So each one thought that her part of the bill was $19 instead of the original $20. with a $5 bill to deliver to the women. The bellhop was dishonest, though, and kept $2 When Franklin heard about this story, he did some calculations: Each woman thought she paid $19, and 3 x S19 is $57. The bellhop kept $2, so S7+$2 59. What happened to the missing dollar? Is Franklin's reasoning right or wrong? Determine what happened to the missing dollar and explain your reasoning

Explanation / Answer

solution=

$19 was the bill the women thought they had paid, and in taking the women's opinion, you ignore the bellhop's $2. The women, whose opinion you're using, don't know about it, so it doesn't exist in the story where each women pays $19. Add back the $3 (3 women x $1 each) and you get 3 x $19 + $3 = $60.

What about the real numbers, not what the women thought they paid? $55/3 per woman x 3 women is $55 total bill minus what they got back, let's add it back. 3 women x $1 per woman + $2 for the bellhop is $5. Add it all together and $55 + $5 is $60

or

There is no missing dollar. The women never paid $60. The woman all paid $19 each, and 3 x 19 = $57. The hotel got $55 of those. The bellhop got the other $2.

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