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Thread: Help with Linear Algebra question

  1. #1
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    Question Help with Linear Algebra question

    I have two more sisters than brothers. Each of my sisters has two more sisters than brothers. How many more sisters than brothers does my youngest brother have?

    I tried solving it by backward method, but I'm not sure if it's the right approach to do.

    If I have brother=1
    then I have 3 sisters.

    I'm not sure how to do it after that. Help would be appreciated!
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  2. #2
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    Re: Help with Linear Algebra question

    Quote Originally Posted by Ibrahimj View Post
    I have two more sisters than brothers. Each of my sisters has two more sisters than brothers. How many more sisters than brothers does my youngest brother have?

    I tried solving it by backward method, but I'm not sure if it's the right approach to do.

    If I have brother=1
    then I have 3 sisters.

    I'm not sure how to do it after that. Help would be appreciated!
    See if you can figure out whether the "I" in the story is male or female. That's a start.
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  3. #3
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    Re: Help with Linear Algebra question

    Whoever is "talking" has to be a Sister...

    S(talking) : B B B S S S S S

    Any B has 2 brothers and 6 sisters.

    ?????????????????????????????????
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  4. #4
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    Re: Help with Linear Algebra question

    Let "x" be the number of boys and "y" the number of girls in the family.
    case 1: "I" am a boy. I have x-1 brothers and y sisters. "I have two more sisters than brothers" so y= (x-1)+ 2. "Each of my sisters has two more sisters than brothers". Each girl has y- 1 sisters and x brothers so y- 1= x+ 2. The first equation reduces to y= x+ 1 and the second to y= x+ 3. There is no x, y pair that satisfies both.

    case 2: "I" am a girl. I have x brothers and y- 1 sisters. "I have two more sisters than brothers" so y- 1= x+ 2. "Each of my sisters has two more sisters than brothers". Each girl has y- 1 sisters and x brothers so y- 1= x+ 2.

    Both of those reduce to y= x+ 3 so there are an infinite number of solutions. Suppose "I" am a girl and the family has 1 boy and 4 girls. I have 1 brother and 3 sisters- two more sisters than brothers as required. Each of my sisters has 3 sisters and 1 brother- two more sisters than brothers. But suppose the family has 2 boys and 5 girls. I have 2 brothers and 4 sisters- two more sisters than brothers. Each of my sisters has 2 brothers and 4 sisters- two more sisters than brothers. Or the family could have 3 boys and 6 girls, etc.
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  5. #5
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    Re: Help with Linear Algebra question

    Quote Originally Posted by DenisB View Post
    Whoever is "talking" has to be a Sister...

    S(talking) : B B B S S S S S

    Any B has 2 brothers and 6 sisters.

    ?????????????????????????????????
    OK so far. Now for your example what is the answer to the question: How many more sisters than brothers does the youngest brother have?
    Once you have that you have to figure out if its the same for different size families. For example, what if you start with the "I", $n$ sisters, and $n-2$ brothers? Can you still show "I" is female and do you get the same final answer?
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  6. #6
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    Re: Help with Linear Algebra question

    Frankly my dear.....
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    Re: Help with Linear Algebra question

    Quote Originally Posted by HallsofIvy View Post
    Both of those reduce to y= x+ 3 so there are an infinite number of solutions.
    BUT there is a limit: normal life span of women in months divided by 9 !!
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  8. #8
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    Re: Help with Linear Algebra question

    But there is only one answer to the OP's question.
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    Re: Help with Linear Algebra question

    Hi
    Thank you all for helping!
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  10. #10
    Member Walagaster's Avatar
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    Re: Help with Linear Algebra question

    Quote Originally Posted by Ibrahimj View Post
    Hi
    Thank you all for helping!
    Are you going to leave us hanging like that? Did you solve it? Are you going to show us what you got and how you did it?
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