## Sally 5 years ago how many gallons of distilled water must be mixed with 50 gallons of 30% alcohol solution to obtain a 25% solution. distilled water is 0% alcohol.

1. anonymous

You need the situation where$(alcohol)/(alcohol+water)=0.25$ Write A for alcohol and W for water. Now, you're not changing the amount of alcohol in the solution, but we need to find out how much you have. From what you're given, currently, $\frac{A}{A+W^*}=\frac{A}{50 gal}=0.3 \rightarrow A=0.3 \times 50gal = 15gal$where we've identified A+W* as the total volume of solution. You need$\frac{A}{A+W^*}=\frac{15}{15+W^*}=0.25$where W* is the amount of total water now needed. Solving for W* gives, $15=.25 \times 15+.25W^*\rightarrow W^*=45gal$Now, this 45 is the final amount of water needed to be present in the solution. You already have (50-15)gal = 35 gal sitting there, so to make water volume equal to 45, you need to add 10 gallons.

2. anonymous

To check, you have 15 gallons of alcohol, and now 45 gallons of water, so your percent volume of alcohol will be,$\frac{15}{15+45}=\frac{15}{60}=\frac{1}{4}=0.25$

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