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Math Help - linear inequality

  1. #1
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    linear inequality

    I got this problem from a guide book.

    Question:
    It is given that -5\le p\le 2 and 3\le q \le 10.
    Find the least posible value of \frac{q-p}{q}

    Answer given in the book is as follows:
    Least possible value \frac{q-p}{q}=\frac{3-2}{10}=\frac{1}{10}

    My question is how can the variable q takes two different values in an algebraic expression.

    Please help.

    Thanks.
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  2. #2
    Senior Member
    Joined
    Nov 2007
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    I don't know how q can take two different values but I have a solution :
    \frac {q-p}q=1-\frac pq So we need to maximize \frac pq. And \frac pq has its maximum when p is the largest possible and q is the least possible. So p=2 and q=3: \frac {q-p}q=\frac {3-2}{3}=\mathbf{\frac 13}

    I now think that I'm right but if not please mention it!
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