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Math Help - equation with integers

  1. #1
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    equation with integers

    Find the whole numbers for A and B that satisfy the following equation.

    A+B = A.B A and B cannot be zero.
    2

    AND

    Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

    A) 110 Years apart?
    B) 11 Years apart?
    C) 10 years apart?
    D) 2 Years apart?


    Thanks SOOOOOO much!
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  2. #2
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    Quote Originally Posted by annie3993 View Post
    Find the whole numbers for A and B that satisfy the following equation.

    A+B = A.B A and B cannot be zero.
    2

    AND

    Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

    A) 110 Years apart?
    B) 11 Years apart?
    C) 10 years apart?
    D) 2 Years apart?


    Thanks SOOOOOO much!
    You have 2 unknowns - A and B, so you need simultaneous equations to find both. 1 equation is not enough.
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by annie3993 View Post
    Find the whole numbers for A and B that satisfy the following equation.

    A+B = A.B A and B cannot be zero.
    2
    Note that A.B can be written as A+\frac{B}{10}

    so now we get

    \frac{A+B}{2}=A+\frac{B}{10} multiply by 10 to clear the fractions

    5A+5B=10A+B \iff -5A=-4B \iff A=\frac{4}{5}B

    Since A need to be a whole number B needs to be a multiple of the denominator 5

    b=5, A=\frac{4}{5}(5)=4

    A=4 and B=5.

    I hope this helps.
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  4. #4
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    i still can't get this one...

    Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

    A) 110 Years apart?
    B) 11 Years apart?
    C) 10 years apart?
    D) 2 Years apart?


    Thanks SOOOOOO much!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by annie3993 View Post
    i still can't get this one...

    Every once in a while a calendar year will be a palindrome, which means it reads the same forward and backward. Starting with 10 a.d. , can you come up with a pair of palindrome years that are...

    A) 110 Years apart?
    B) 11 Years apart?
    C) 10 years apart?
    D) 2 Years apart?


    Thanks SOOOOOO much!
    If there is an algorithm to determin this I do not know it.

    You just have to guess(make educated guesses) and check

    for exapmle for D)

    1001 is a one and two less than it is 999.

    Write some out and see what you can get
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  6. #6
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    Smile Thanx

    Alright, i'll try that. Thanx 4 your help!
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  7. #7
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    How does A.B = A + B/10?

    :S


    A.B = A*B, no?

    I don't get this.
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  8. #8
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    Wink

    i don't really get it either, but i desperately need extra credit, so i'll take any answer...
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  9. #9
    Behold, the power of SARDINES!
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    Quote Originally Posted by sean.1986 View Post
    How does A.B = A + B/10?

    :S


    A.B = A*B, no?

    I don't get this.

    A and B are digits the peroid doesn't represent multiplication.

    The period is a decimal point so what the question is asking is

    \frac{4+5}{2}=4.5

    \frac{9}{2}=4.5

    4.5=4.5

    I hope this clears it up.
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  10. #10
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    Yes it does, haha. I thought it was multiply.
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  11. #11
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    Cool

    A) 1221 1331
    B) 22 11
    C) 121 131
    D) 1001 999
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  12. #12
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    Quote Originally Posted by TheEmptySet View Post
    A and B are digits the peroid doesn't represent multiplication.

    The period is a decimal point so what the question is asking is

    \frac{4+5}{2}=4.5

    \frac{9}{2}=4.5

    4.5=4.5

    I hope this clears it up.
    For extra credit problems we should only be giving hints and commenting on solutions proposed by the original poster.

    Giving them a full answer that can be handed in is helping no one, whatever the original poster thinks.

    RonL
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