Results 1 to 4 of 4

Math Help - Find individual ages of the ten persons?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Find individual ages of the ten persons?

    In a group of 10 persons, each person is asked to write the sum of ages of all the other 9 persons. If all the ten sums form a 9-elements set{82,83,84,85,87,89,90,91,92}, then find the individual ages of the ten persons.

    Please explain the method explicitly while finding the solution.Thanks.
    Last edited by fardeen_gen; August 6th 2008 at 05:30 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by fardeen_gen View Post
    In a group of 10 persons, each person is asked to write the sum of ages of all the other 9 persons. If all the ten sums form a 9-elements set{82,83,84,85,87,89,90,91,92}, then find the individual ages of the ten persons.
    If all ten sums are added together, the result will be the sum of the ten ages multiplied by 9 (since each person's age will have been counted nine times).

    In the 9-element set{82,83,84,85,87,89,90,91,92}, one item must obviously be duplicated. The sum of the nine elements is 783, which is already a multiple of 9. So the duplicated element must also be a multiple of 9. The only possibility for this element is that it is 90. Thus 9 times the sum of the ages is 783+90 = 873.

    That should be quite enough of a hint to enable you to solve the problem.

    Edit. The problem says that "each person is asked to write the sum of ages of all the other 9 persons." The solution gives the age of the youngest person as 5. How many five-year-olds do you know who could correctly add nine numbers ranging from 6 to 15 and then write down the result? That makes the problem seem unrealistic to me.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539
    Can you please explain how one item must obviously be duplicated?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by fardeen_gen View Post
    Can you please explain how one item must obviously be duplicated?
    You are told that all ten people were asked to write a number. But the set of numbers only contains nine elements. So one number must have occurred twice.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distribute subjects' ages for most Power
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 22nd 2011, 04:13 PM
  2. Find total sales and individual sales
    Posted in the Business Math Forum
    Replies: 5
    Last Post: April 8th 2011, 03:31 PM
  3. Worded problem - ages of a lot of people.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 21st 2011, 12:23 PM
  4. Replies: 2
    Last Post: October 24th 2008, 12:58 PM
  5. ages problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 24th 2008, 08:55 AM

Search Tags


/mathhelpforum @mathhelpforum