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solutions of 30% and 90% acid as well as all of the distilled water he wants. Set-up and solve a
system of linear equations which determines all of the possible combinations of the stock solutions
and water which would produce the required solution.
Solution. We are after three unknowns, the amount (in mL) of the 30% stock solution (which
we’ll call x), the amount (in mL) of the 90% stock solution (which we’ll call y ) and the amount
(in mL) of water (which we’ll call w). We now need to determine some relationships between these
variables. Our goal is to produce 500 milliliters of a 40% acid solution. This product has two
deﬁning characteristics. First, it must be 500 mL; second, it must be 40% acid. We take each
13 Here, any choice of s and t will determine a solution which is a point in 4-dimensional space. Yeah, we have
trouble visualizing that, too. 8.1 Systems of Linear Equations: Gaussian Elimination 461 of these qualities in turn. First, the total volume of 500 mL must be the sum of t...
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