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Math Help - Problem solving question help...

  1. #1
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    Problem solving question help...

    A students scores on the first three tests in a math course are 65,75 and 87. What range of scores on a fourth test will give the student an average that is less than 80 but no less than 70 for the four tests?

    65+75+87+x/4 < 79.9, x<92.6

    65+75+87+x/4 >(and equal to) 70, x>(and equal to) 53

    So the range of scores would be 53 to 92.6? Is this correct and am I writing this down correctly?

    Thank you very much
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  2. #2
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    Re: Problem solving question help...

    now for the conditions you have stated, the inequalities are:
    80>\frac{65+75+87+x}{4}>70 where x is the marks in the fourth subject.
    \implies 320>65+75+87+x and 65+75+87+x>70 \implies 93>x and x>53 (after solving the two inequalities).
    therefore the range of marks to satisfy the stated condition are (93,53), the open interval from 53 to 93,i.e every number possible between 53 and 93 but without 53 and 93 itself.
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  3. #3
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    Re: Problem solving question help...

    Hello, curt26!

    A student's scores on the first three tests in a math course are 65, 75 and 87.
    What range of scores on a fourth test will give the student an average
    that is less than 80 but no less than 70 for the four tests?

    Let x = his score on the fourth test.

    His average will be: . \frac{65 + 75 + 87 + x }{4} \:=\:\frac{x+230}{4}

    He wants his average to be at least 70 and less than 80.

    Hence, we have: . 70 \;\le\;\frac{x+{\color{red}227}}{4}\;<\;80

    Multiply by 4: . 280 \;\le\;x+{\color{red}227} \;<\;320

    Subtract 227:. . . . {\color{red}53} \;\le\;x\;<\;{\color{red}93}

    Last edited by Soroban; April 8th 2013 at 07:50 PM. Reason: Corrected my silly error.
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  4. #4
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    Re: Problem solving question help...

    Except 65 + 75 + 87 = 227, not 230.
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  5. #5
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    Re: Problem solving question help...

    Thank you so much you guys!
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