My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news

Thanks Tree5Thanks
  • 4 Post By skipjack
  • 1 Post By Denis
LinkBack Thread Tools Display Modes
April 16th, 2016, 05:32 AM   #1
Joined: Apr 2016
From: United Kingdom

Posts: 1
Thanks: 0

Physics Grad Stumped By A 12 Year Old's Math Problem

I am a little embarrassed that I have been unable to answer this question from my 12 year old son's Maths exam paper. I felt it was too tough for a 12 year old. Can anyone solve it?

Erdos runs a Maths Club. Each time they meet, they each drink a pint of coffee with milk. The amounts of coffee and milk may vary from cup to cup, but are never zero. Erdos drinks a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the club (including Erdos)? Make your reasoning clear.

It seems to present ONE equation, but with two unknown quantities. Conventional wisdom would therefore suggest the problem is impossible to solve.

Last edited by skipjack; April 16th, 2016 at 08:35 PM.
IqbalHamid is offline  
April 16th, 2016, 06:46 AM   #2
Senior Member
Joined: Dec 2015
From: holland

Posts: 162
Thanks: 37

Math Focus: tetration
12N = 3m + 2c
(3m + 2c)/12 = a natural number

It is undetermined.

Last edited by skipjack; April 16th, 2016 at 06:56 AM.
manus is offline  
April 16th, 2016, 07:13 AM   #3
Global Moderator
Joined: Dec 2006

Posts: 20,978
Thanks: 2229

Suppose they drink m pints of milk and c pints of coffee in total, where m > 0 and c > 0.

From what is stated about Erdos, m/4 + c/6 = 1.

Hence m = 4 - 2c/3 and so is less than 4.

If there are n other club members, n = (3/4)m + (5/6)c = (3/4)m + 5(1 - m/4) = 5 - m/2.

As n is a whole number, m is a multiple of 2.

As it's already known that m > 0 and m < 4, it follows that m = 2.

Hence n = 4, which means that the club has 5 members in total.
Thanks from jonah, Denis, 123qwerty and 1 others
skipjack is offline  
April 16th, 2016, 10:20 AM   #4
Math Team
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Just brilliant, Skip...I'm sure Iqbal will buy you an extra large coffee
Thanks from jonah
Denis is offline  
April 16th, 2016, 06:15 PM   #5
Senior Member
Joined: Jan 2014
From: The backwoods of Northern Ontario

Posts: 393
Thanks: 71

I don't understand skipjack's solution. So I tried to verify his answer.

However, I am unable to do that either.

Would someone please write out a verification?

I'd probably fail that Grade 7 math exam.

Last edited by skipjack; April 16th, 2016 at 09:18 PM.
Timios is offline  
April 16th, 2016, 09:27 PM   #6
Global Moderator
Joined: Dec 2006

Posts: 20,978
Thanks: 2229

Originally Posted by Timios View Post
I don't understand...
It is necessary to assume that 1 pint was the total of coffee and milk together that each drank, and that the overall totals ignore any wasted coffee or milk (or no wastage occurred), so that n + 1 = m + c, then subtracting 1 = m/4 + c/6 gives n = (3/4)m + (5/6)c, etc. Are there any later steps you didn't understand?

Last edited by skipjack; April 17th, 2016 at 11:44 AM.
skipjack is offline  

  My Math Forum > Math Forums > Math

club, coffee, erdos, grad, how many, math, maths, physics, problem, stumped, year

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Matrix Problem I am stumped on dollwonderland Pre-Calculus 1 January 25th, 2015 06:38 PM
1st year math - Riemann zeta function & series lun123 Real Analysis 6 November 11th, 2013 10:21 AM
Very Stumped on This Limit Problem soulrain Calculus 4 June 4th, 2012 06:58 PM
1st year physics maapony Algebra 2 September 1st, 2011 02:44 PM
A problem that has me rather stumped. GMNives Algebra 1 May 10th, 2008 02:13 PM

Copyright © 2019 My Math Forum. All rights reserved.