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Math Help - Mixture (%) Word Problem

  1. #1
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    Mixture (%) Word Problem

    I'm struggling on how to set up this word problem; I've tried following examples from similar problems, but there are phrases in this one that throw me off.

    Industrial biochemists routinely use a machine to mix a buffet of 10% acetone by adding 100% acetone to water. One day, instead of adding 5 L of acetone to create a vat of buffer, a machine added 10 L. How much additional water was needed to bring the concentration down to 10%

    A thanks in advance for the help.
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by CODEONE View Post
    I'm struggling on how to set up this word problem; I've tried following examples from similar problems, but there are phrases in this one that throw me off.

    Industrial biochemists routinely use a machine to mix a buffet of 10% acetone by adding 100% acetone to water. One day, instead of adding 5 L of acetone to create a vat of buffer, a machine added 10 L. How much additional water was needed to bring the concentration down to 10%

    A thanks in advance for the help.
    5 liters of acetone is 10% of the total mix.
    5 = .1t

    multiply by ten to find how many liters are in the total mix
    50=t

    so they normally have a total of 50 liters. The total mix is the sum of the acetone and the water so 5+w=50 then w = 50-5 then w=45. So they normally ad 45 liters of water to 5 liters of acetone to get a mix of 10% acetone.

    However, this time they added 10 liters instead of 5. But they want it to still equal 10% of the total mix, so using the same concept 10=.1t then 100=t. So this new mix must have 100 liters. 100 liters minus 10 liters of acetone is 90 liters. 90 liters minus the initial 45 liters of water is 45 liters. So they must add an additional 45 liters of water to get a mixture of 10% acetone.
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