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Math Help - Systems of Equations word problem

  1. #1
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    Systems of Equations word problem

    Hello,

    Will anyone help me set these two problems up? tHanks so muchhhh!!!

    1. John can paint a house in 30 hours and Jerald can paint a house in 5 hours. How long would it take the two of them to paint a house together?

    2. In mixing some fuel, a scientist combines a 50% ethanol sotluion with a 90% ethanol solution to get 40 liters 80% ethanol solution. How much of the 50% solution did the scientist use in the mixture?
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  2. #2
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    Quote Originally Posted by jenjen View Post
    Hello,

    Will anyone help me set these two problems up? tHanks so muchhhh!!!

    1. John can paint a house in 30 hours and Jerald can paint a house in 5 hours. How long would it take the two of them to paint a house together?

    2. In mixing some fuel, a scientist combines a 50% ethanol sotluion with a 90% ethanol solution to get 40 liters 80% ethanol solution. How much of the 50% solution did the scientist use in the mixture?
    1.
    In 1 hour, John and Jerald can paint \frac{1}{30} and \frac{1}{5} of the house, respectively.
    If they do it together for 1 hour, they can paint \frac{1}{30} + \frac{1}{5} of the house, or \frac{7}{30}
    Let H be the number of hours for them working together:
    \frac{7}{30} x H = 1
    where 1 represent 100% of the work (painting the house)
    Therefore, H = \frac{30}{7} hours or 4\frac{2}{7} hours
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  3. #3
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    Quote Originally Posted by jenjen View Post
    2. In mixing some fuel, a scientist combines a 50% ethanol sotluion with a 90% ethanol solution to get 40 liters 80% ethanol solution. How much of the 50% solution did the scientist use in the mixture?
    Let x and y be volumes (L) of 50% and 90% solutions used, respectively.
    x + y = 40 ...(1)
    0.5x + 0.9y = 0.8(x + y)
    5x + 9y = 8x + 8y
    y = 3x ...(2)

    (2) into (1) you have 4x = 40, hence x = 10 (litres)
    and y = 30 litres
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  4. #4
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    Talking

    To learn how to set these up for yourself (that is, to learn the reasoning by which they obtained the hand-in solutions they provided), try this lesson on "work" problems and this lesson on "mixture" problems.
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