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25 October, 21:01

A lab needs a 20 liters of a 15% acid solution. The lab only has a 10% acid solution and a 30% acid solution. How much of the 10% acid solution will they need to mix with the 30% solution to obtain 20 liters of a 15% solution?

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  1. 25 October, 21:28
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    To start, it's always easiest to turn percentages into decimals - so let's do that first:

    10% Weak solution =.1

    30% Strong solution =.3

    15% Medium solution =.15

    Next we need to assign a value to the amount of each solution we have or need.

    Weak solution = x (because we don't yet know how much we need, we give it a variable)

    Strong solution = 20-x (because once we determine x and know there are 20 total liters, we can simply subtract to figure out the remainder)

    Medium solution = 20 (because in total we need 20 liters)

    Now we create the formula to solve for x.

    .1x+.3 (20-x) =.15 (20)

    x=15

    So you would need 15 liters of the weaker 10% solution and 5 liters of the stronger 30% solution. This makes sense b/c the average 15 is much lower than 30 so we'd expect to need much more of the weaker solution.
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