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Math Help - Absolutely no idea how to do this

  1. #1
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    Absolutely no idea how to do this

    How many natural numbers less than 200 leave a remainder of 3 when divided by 7 and a remainder of 4 when divided by 5?
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  2. #2
    Junior Member
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    For the remainder of 3 when divided by 7, look at numbers of the form 7n+3,
    the first few are 3,10,17,... get the idea now? You can do the same thing for the ones that leave a remainder of 4 when divided by 5. Then what you can do is compare the two lists and see what numbers are the same.
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  3. #3
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    Thanks, but my teacher doesn't like it when we do trial and error (I mean just comparing two lists) it has to be "clean."

    But I like the 7n+3. Would this work?

    x=7n+3
    x=5n+4

    0=2n-1
    -2n=-1
    2n=1
    n=1/2

    Well that didn't work is there something kind of like that I could do though?
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