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Thread: 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:
    $\displaystyle 80>\frac{65+75+87+x}{4}>70$ where x is the marks in the fourth subject.
    $\displaystyle \implies 320>65+75+87+x $and $\displaystyle 65+75+87+x>70 \implies 93>x$ and $\displaystyle x>53$ (after solving the two inequalities).
    therefore the range of marks to satisfy the stated condition are $\displaystyle (93,53)$, 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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    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 $\displaystyle x$ = his score on the fourth test.

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

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

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

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

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

    Last edited by Soroban; Apr 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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