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Math Help - Word problems

  1. #1
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    Word problems

    1. The cooling system of Alex's car holds 10 quarts. It is now filled with a mixture that is 60% water and 40% antifreeze. Hearing a weather forecast for severe cold, Alex decides to increase the strenth of the antifreeze mixture to 50%. To do this, Alex must drain off a certain number of quarts from the cooling system and then replace them by pure antifreeze. How many quarts must be drained?

    0.6w + 0.4a = 0.5 ?

    I know 6 quart will be water and 4 quart antifreeze so if I drain one quart
    I will have 5.4 water and 3.6 antifreeze then I can add 1 antifreeze to make 5.4 w and 4.6 antifreeze. I know I have to do this until I make 5 water and 5 antifreeze. I tried to set up an equation to make it easier but I can't do it.


    2.Taylor works after school in a health food store, where one of the more challenging tasks is to add cranberry juice to apple juice to make a cranapple drink. A liter of apple juice costs $0.80 and a liter of cranberry juice costs $1.25. The mixture is to be sold for exactly the cost of the ingredients, at $1.09 per liter. How many liters of each juice should Taylor use to make 20 liters of the cranapple mixture?

    0.8A + 1.25c = 21.80

    Am I supposed to guess and check from here?
    I tried 10 liters each and it is 8 + 12.50 = 20.50
    Can someone show me a better way to do this?


    Vicky.

    I really appreciate the help I get!!!
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  2. #2
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    Quote Originally Posted by Vicky1997 View Post
    1. The cooling system of Alex's car holds 10 quarts. It is now filled with a mixture that is 60% water and 40% antifreeze. Hearing a weather forecast for severe cold, Alex decides to increase the strenth of the antifreeze mixture to 50%. To do this, Alex must drain off a certain number of quarts from the cooling system and then replace them by pure antifreeze. How many quarts must be drained?

    0.6w + 0.4a = 0.5 ?

    I know 6 quart will be water and 4 quart antifreeze so if I drain one quart
    I will have 5.4 water and 3.6 antifreeze then I can add 1 antifreeze to make 5.4 w and 4.6 antifreeze. I know I have to do this until I make 5 water and 5 antifreeze. I tried to set up an equation to make it easier but I can't do it.


    2.Taylor works after school in a health food store, where one of the more challenging tasks is to add cranberry juice to apple juice to make a cranapple drink. A liter of apple juice costs $0.80 and a liter of cranberry juice costs $1.25. The mixture is to be sold for exactly the cost of the ingredients, at $1.09 per liter. How many liters of each juice should Taylor use to make 20 liters of the cranapple mixture?

    0.8A + 1.25c = 21.80

    Am I supposed to guess and check from here?
    I tried 10 liters each and it is 8 + 12.50 = 20.50
    Can someone show me a better way to do this?


    Vicky.

    I really appreciate the help I get!!!


    I know 6 quart will be water and 4 quart antifreeze so if I drain one quart
    I will have 5.4 water and 3.6 antifreeze then I can add 1 antifreeze to make 5.4 w and 4.6 antifreeze. I know I have to do this until I make 5 water and 5 antifreeze.


    If you continue this method (it is tedious), drain 1.5 quarts & replace, then drain 2 quarts & replace, then 2.5 quarts & replace, etc.

    If you do this, you should become aware of the resulting equation that you are seeking.

    AND probably you will never forget how to construct the equation directly from the data given.
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  3. #3
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    Could you please show me the equations for 1 and 2?

    Vicky.
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  4. #4
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    Can someone show me how to set up the two equations please?

    Vicky.
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  5. #5
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    Quote Originally Posted by Vicky1997 View Post
    1. The cooling system of Alex's car holds 10 quarts. It is now filled with a mixture that is 60% water and 40% antifreeze. Hearing a weather forecast for severe cold, Alex decides to increase the strenth of the antifreeze mixture to 50%. To do this, Alex must drain off a certain number of quarts from the cooling system and then replace them by pure antifreeze. How many quarts must be drained?

    2.Taylor works after school in a health food store, where one of the more challenging tasks is to add cranberry juice to apple juice to make a cranapple drink. A liter of apple juice costs $0.80 and a liter of cranberry juice costs $1.25. The mixture is to be sold for exactly the cost of the ingredients, at $1.09 per liter. How many liters of each juice should Taylor use to make 20 liters of the cranapple mixture?
    1. let x = number of qts to drain and fill

    (10 qts at 40%) - (x qts at 40%) + (x qts at 100%) = (10 qts at 50%)

    10(.40) - x(.40) + x(1.00) = 10(.50)

    solve for x


    2. let x = liters of apple

    20-x = liters of cranstuff

    x(.80) + (20-x)(1.25) = 20(1.09)

    solve for x


    btw ... don't bump, it's against the rules here.
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