Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

Help with algebra?

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  • 4 weeks ago

    I'm not sure why we'd want to "make a chart,"  

    but perhaps if I show you an algebraic solution, 

    your class experience will suggest a suitable chart. 

     

    Let a represent the quantity of solution A, in liters, 

    and b represent the quantity of solution B. 

     

    Then we can write the equations 

    a + b = 4 [describing the total quantity of solution] 

    and 

    0.08a + 0.20b = 0.11 (4) [describing the acetic acid percentage] 

    to represent the problem. 

     

    We can simplify that second equation, dividing each side by 0.04 to obtain 

    2a + 5b = 11 

    and then find the common solution. Subtracting twice the first equation yields 

    3b = 3 

    or 

    b = 1 

    which leads quickly to the answer, that we combine 

    3 liters of solution A (contributing 0.24 liters acetic acid) 

    and 

    1 liter of solution B (contributing 0.20 liters acetic acid) 

    to obtain 4 liters of solution with 0.44 liters (11%) acetic acid. 

     

    Back to the chart question: Perhaps you could make a table with different quantities of each solution and calculate the acid percentage in each. 

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  • 4 weeks ago

    Let z be the volume of Solution A (in liters) to be found.

    Then the volume of Solution B is (4 - z) liters.

    (0.08 z) + (0.20 (4 - z)) = 4 (0.11)

    Solve for z algebraically:

    z = 3 liters Solution A

    4 - z = 1 liter Solution B

    Make the chart yourself.

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