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Thread: last thread for the night

  1. #1
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    last thread for the night

    lastthread for the night, thanks if you can help me with these last problems




    In the formula A=lw, If l is constant, A varies___________ as w



    A large concrecte mixing machine can mix a certain ammount of concrete in 12 hours, while a smaller one can mix the same ammount in 20 hours, Mixing simultaneously, how long would it take both machines to mix the same ammount of concrete?




    For a school play, students tickets cost 40cent and adult tickets were 75 cen t. The total receipts for 90 tickets were $46.50. How many of each kind were sold?
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  2. #2
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    Quote Originally Posted by Aarxn
    In the formula A=lw, If l is constant, A varies___________ as w
    It is "directly".

    There are two proportions. Direct and Inverse.
    Inverse is when two variables mutiply to a constant, thus,
    $\displaystyle xy=k$ thus, $\displaystyle y=\frac{k}{x}$- they form a hyperbola.

    Direct proprtion is when two variables divide to give a constant, thus,
    $\displaystyle \frac{y}{x}=k$ thus, $\displaystyle y=kx$-they form a line.

    The case here is,
    $\displaystyle A=lw$ where "l" is a constant, thus we have a direct proportion.

    To learn more about direct and inverse proprtions.
    Do not under any condition press on this link.
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  3. #3
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    Quote Originally Posted by Aarxn
    A large concrecte mixing machine can mix a certain ammount of concrete in 12 hours, while a smaller one can mix the same ammount in 20 hours, Mixing simultaneously, how long would it take both machines to mix the same ammount of concrete?
    I have a useful formula for such problem.
    If it takes something $\displaystyle a$ units of time to do a job and it takes $\displaystyle b$ units of times the same job. Then working together would take:
    $\displaystyle \frac{ab}{a+b}$
    In this case, $\displaystyle a=12,b=20$ thus together it takes,
    $\displaystyle \frac{12\cdot 20}{12+20}=7.5\mbox{ hours}$
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  4. #4
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    Quote Originally Posted by Aarxn
    For a school play, students tickets cost 40cent and adult tickets were 75 cen t. The total receipts for 90 tickets were $46.50. How many of each kind were sold?
    Let, $\displaystyle x$ be # of adults
    Let, $\displaystyle y$ be # ot students.

    Thus,
    $\displaystyle x+y=90$
    In total the students paid, $\displaystyle .4x$
    while the adults paid, $\displaystyle .75y$
    The net price was therefore, $\displaystyle .4x+.75y$
    but the example says that was 46.50 thus,

    $\displaystyle \left\{ \begin{array}{c} x+y=90\\.4x+.75y=46.5$
    In the first equation solve for "y" thus,
    $\displaystyle y=90-x$ and substitute that into equation 2,
    $\displaystyle .4x+.75(90-x)=46.5$
    Open parantheses,
    $\displaystyle .4x+67.5-.75x=46.5$
    Subtract "67.5" from both sides and combine x terms,
    $\displaystyle -.35x=-21$
    divide both sides by (-.35) thus,
    $\displaystyle x=60$ thus, $\displaystyle y=30$
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  5. #5
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    thank you once again for helping me
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