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Math Help - Determine an equation

  1. #1
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    Determine an equation

    Hey guys,

    the task:
    If you drink a cola and an energy drink, you consume 111 mg of caffeine. The energy drink has 6 more than twice the number of mg of caffeine as compared to the cola.
    Use a system of equations and a graph to determine how many milligrams of caffeine are in an energy drink and a cola. Verify your answer.

    Lets say c = cola and e = energy

    Equation: c + e = 111 and c + 2e + 6 = 111

    Are the equations right? How can get the task done?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Determine an equation

    Your first equation is correct, but the second is not. Let's look at the statement:

    The energy drink has 6 more than twice the number of mg of caffeine as compared to the cola.

    The energy drink: e

    has: =

    6 more: +6

    than twice the number of mg of caffeine as compared to the cola: 2c

    Putting this together into an equation, we have:

    e=2c+6

    Now, substitute this into the first equation for e to get:

    c+(2c+6)=111

    Solve this for c, then use the equation e=2c+6 to find e.
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  3. #3
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    Re: Determine an equation

    Hey ford2008.

    The idea you have is correct but in your second equation having 6 more than twice the number means that e = 6 + 2c or c = 6 + 2e (it doesn't matter which one you choose). This would make the second equation c + 2c + 6 = 111 or 3c + 6 = 111.
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  4. #4
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    Re: Determine an equation

    Does anyone know how to make a graph out of these 2 equations?
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Determine an equation

    Which variable do you want to be independent?
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  6. #6
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    Re: Determine an equation

    the variable c+e=111 should be the independent.
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Determine an equation

    I mean which variable c or e do you want to be independent, that is will represent the horizontal axis?
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  8. #8
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    Re: Determine an equation

    I want the variable c to be independent.
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  9. #9
    MHF Contributor MarkFL's Avatar
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    Re: Determine an equation

    When I graph linear equations, I find the easiest way is to write the equations in slope-intercept form. For your system, this would be:

    (1) e=-c+111

    (2) e=2c+6

    To graph (1), we now simply plot the point (0,111) then move 1 unit to the right and 1 unit down to the point (1,110) and plot this. Now draw the line that contains these two points.

    To graph (2), plot the point (0,6). then move 1 unit to the right and 2 units up to the point (1,8) and plot this. Then draw the line containing these two points.
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