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Math Help - Find the value for p

  1. #1
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    Find the value for p

    If p is an integer and 3 is the remainder when 2p+7 is divided by 5, then what is the value of p?

    Here is my steps:
    (2p+7)/5 = 3
    2p+7= 15
    2p= 8
    p=4

    I don't know where I got wrong but the correct answer is 3

    Thanks in advance
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  2. #2
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    Quote Originally Posted by fabxx View Post
    If p is an integer and 3 is the remainder when 2p+7 is divided by 5, then what is the value of p?

    Here is my steps:
    (2p+7)/5 = 3 Mr F says: This is wrong. It's saying that 5 goes into 2p + 7 three times rather than 3 is the remainder ..... Your starting point should be (2p+7) = 5n + 3 where n is a positive integer.

    2p+7= 15
    2p= 8
    p=4

    I don't know where I got wrong but the correct answer is 3

    Thanks in advance
    By the way, I should add that there are an infinite number of solutions for p, not just one as your question implies.
    Last edited by mr fantastic; September 20th 2008 at 03:23 AM. Reason: Added the by the way ...... I wonder if I beat CB's reply (whatever it may be). And ticbol's. And Matt's. Popular question.
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  3. #3
    Super Member Matt Westwood's Avatar
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    You're going to ask me why, but you "can't do" \frac {2p + 7} 5 = 3 for determining the remainder when 2p+7 is divided by 5.

    What \frac {2p + 7} 5 = 3 means is that 3 is the result of dividing 2p+7 by 5.

    What you want to say is something like this.

    When you divide 2p+7 by 5, you get some integer (call it q) plus 3 left over.

    Thus 2p+7 = 5q + 3.

    (Or you could say: if you subtract 3 from 2p+7, then its remainder when divided by 5 will be zero, so 2p+7 - 3 is an exact multiple of 5.)

    So you have 2p+4 = 5q and so p+2 = 5q / 2.

    So you know that q must be an even number or 5q/2 won't be an integer.

    So you also got (p+2) / 5 = q

    You can also see that p+2 must be divisible by 5, or q won't be an integer either.

    Turns out there are lots of answers to this problem, but the simplest one is a value of p such that p+2 is divisible by 5. So see what happens if you pick p+2 = 5.
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