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anonymous
 one year ago
Liquid X is composed of 30% alcohol and 70% water, while Liquid Y is composed of 18% alcohol and 82% water. The two liquids are combined to form Mixture Z, which is composed of 21% alcohol and 79% water. What is the ratio in Mixture Z of Liquid X to Liquid Y?
anonymous
 one year ago
Liquid X is composed of 30% alcohol and 70% water, while Liquid Y is composed of 18% alcohol and 82% water. The two liquids are combined to form Mixture Z, which is composed of 21% alcohol and 79% water. What is the ratio in Mixture Z of Liquid X to Liquid Y?

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ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Let \(a\) be the amount of solution \(X\) in \(Z\) and \(b\) be the amount of solution \(Y\) in \(Z\). \(A\) is Alcohol and \(W\) is water. Then $$ X=0.3A+.7W\\ Y=.18A+.82W\\ Z=.2A+.79W=aX+bY\\ =a(0.3A+.7W)+b(.18A+.82W)\\ =A(.3a+.18b)+W(.7a+.82b) $$ This means that $$ Z=.2A+.79W=A(.3a+.18b)+W(.7a+.82b)\\ \implies \\ .2=(.3a+.18b)\\ .79=(.7a+.82b) $$ Two equations. Two unknowns. Solvable. When you get a and b you can then determine the ratio of X to Y in Z: $$ \frac{a}{b} $$ Does this make sense?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1*Above \(Z=.2\color{red}1A+.79W\)  notice I missed the "1"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmmm I'm going to have to look at this several times ....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hey this is a hard problem right? It's not just me right?
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