Missing Dollar?!

Hey Brilliant users,

I have recalled a problem I have heard about when I was in 6th grade. The problem goes like this:

3 men rent a room for a hotel. The hotel worker charges them $30.00, and the 3 men split the price equally- each man pays $10.00. Of course, the hotel worker was inexperienced, and the price was actually $25.00. So, the hotel manager tell the worker to give them back the 5 dollars he owed. The worker obviously was mad that he couldn’t get 5 extra dollars. So, he decided to keep 2 dollars, and give the 3 men 3 dollars back. So now, each man has paid $9.00 for the hotel. 9*3=27 dollars, and the worker has 2 dollars. So where did the one dollar go?!

What happened?

#Algebra #Calvinlin #Diamond #Diamond7

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

It is a nice play with words.The sum wont be equal to 30 after redistribution as $10+10+10= 25+3+2$ Now, the hotel kept 25 ,3 were given back and waiter kept 2.

$10-1+ 10-1+10-1=25+2$ Now note that effectively the men have paid $27. Which is consistent with $25 to hotel & $2 to the waiter. I hope its convincing enough

Siddharth Bhatnagar - 6 years ago

Each man has PAID $9. But at the end, they only have $3.

$3 + $25 + $2 = $30.

Ashwin Padaki - 6 years ago

Sorry Jonathan, but how come only Lexingtonians solve your problems? I am kinda skeptical...

Jack H. - 6 years ago

I am sorry Jack, my friends on brilliant are always being mean and cheating on my problems. They don't even know how to solved them, I am sorry about that. All of my level 4 and above problems are like this.

Jonathan Hsu - 6 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$