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19 April, 16:09

You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you need to add to the mixture

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  1. 19 April, 16:21
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    1.25 cups

    Step-by-step explanation:

    The inicial concentration of the 10 cups of mixture is 10% of white vinegar and 90% water. We can then calculate the number of cups of white vinegar in the mixture:

    Amount of white vinegar = 10% of 10 cups = 1 cup of white vinegar

    Concentration of white vinegar = 1/10 (cups of white vinegar over cups of mixture

    So, if we want to add white vinegar (x cups) until the mixture will be 20% white vinegar and 80% water, we have that:

    Amount of white vinegar = (1+x) cups of white vinegar

    Total number of cups in the mixture = 10+x

    Concentration of white vinegar = 20% = (1+x) / (10+x)

    (1+x) / (10+x) = 0.2

    1 + x = 2 + 0.2x

    0.8x = 1

    x = 1.25 cups

    You need to add 1.25 cups of white vinegar.
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