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Math Help - Solve this and you are a genius

  1. #1
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    Solve this and you are a genius


    What is the solution?
    -*geniuises is not the answer to all question but the question to all answer*
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  2. #2
    Member Henderson's Avatar
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    Start by noticing that algebraically, your statement translates to :
    2 < \frac{88+n}{19+n} < 7 (Do you see why?)

    We'll solve the left side first:
    2 < \frac{88+n}{19+n}
    2(19+n) < 88+n (Since n is positive, 19+n is also positive, and we don't need to worry about direction of the inequality.)
    38+2n < 88+n
    n < 50

    On the right side:
    \frac{88+n}{19+n} < 7
    88+n < 7(19+n)
    88+n < 133+7n
    -45 < 6n
    -7.5 < n

    So -7.5 < n < 50. Since you said n is a positive integer, we'll adjust to 0 < n < 50, of which there are 49 of them (0 and 50 aren't included).
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  3. #3
    Member courteous's Avatar
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    Quote Originally Posted by Henderson View Post
    Start by noticing that algebraically, your statement translates to :
    2 < \frac{88+n}{19+n} < 7 (Do you see why?)
    I don't see why. Please explain.
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  4. #4
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    Hello, hotgal24!

    Find the number of possible positive integers n such that

    there are exactly two positive integers between \frac{88+n}{19+n} and \frac{88}{19}

    Since \frac{88}{19} \:\approx\:4.63, the two positive integers are 3 and 4

    . . and: . \frac{88+n}{19+n} \:>\:2 \quad\Rightarrow\quad n \:<\:50


    Therefore: .  n \:=\:1,2,3, \hdots 49

    . . There are 49 possible values of n.

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