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Math Help - number theory

  1. #1
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    number theory

    although i'm taking a number theory course, but i'm not sure what does the following question do with number theory. Please take a look,

    A piggy bank contains 24 coins, all of which are nickels, dimes, or quarters. If the total value of the coins is two dollars, what combinations of coins are possible?

    Sounds like it's a stat question, thanks for helping.
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  2. #2
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    Quote Originally Posted by suedenation View Post
    although i'm taking a number theory course, but i'm not sure what does the following question do with number theory. Please take a look,

    A piggy bank contains 24 coins, all of which are nickels, dimes, or quarters. If the total value of the coins is two dollars, what combinations of coins are possible?

    Sounds like it's a stat question, thanks for helping.
    This is a linear diopahantine equation.

    Let x,y,z represent the amount of nickels dimes and quaters respectively.
    Then,
    x+y+z=24
    You also know that,
    5x+10y+25z=200
    Thus,
    x+2y+5z=40
    Solve for x in first equation,
    x=24-y-z
    Thus,
    24-y-z+2y+5z=40
    Thus,
    y+4z=16
    Since,
    gcd(1,4)=1 which divides 40 there is a solution.
    The rest is up to you to solve this.

    If you are interesting this is called, Bezout's Identity
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