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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?

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1. ybarrap

Let $$a$$ 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?

2. anonymous

what is the Y?

3. anonymous

oh nvm i see it

4. ybarrap

*Above $$Z=.2\color{red}1A+.79W$$ -- notice I missed the "1"

5. anonymous

hmmmm I'm going to have to look at this several times ....

6. ybarrap

OK

7. anonymous

Hey this is a hard problem right? It's not just me right?

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