A winemaker wants to mix a $10\%$ alcohol wine with $20 \text{ kg}$ of a $55\%$ wine to make a $35\%$ wine cooler. How much of the $10\%$ should be used?
I started with $.1x+.55y=.35$ then I'm not sure how to proceed. They should tell me the $10\%$ amount or $35%$ amount.
The same thing seems to be happening with the following. How much pure alcohol must be added to $40 \text{ oz}$ of a $25\%$ alcohol solution to produce a mixture that is $40\%$ alcohol?
I started with $x+.25y=.4$ , so shouldn't they tell me the total amount or pure amount?
Either I forgot it over the summer, or the homework is missing a part.
Mixture problems make more sense if you organize the information into a chart:
$wt\ \ \ \ \ \ \ \ \ \ \ \%\ \ \ \ \ \ \ \ \ pure EtOH$
$20\ \ \ \ \ \ \ \ \ \ 0.55\ \ \ \ \ \ \ \ \ \ 20(.55) $
$x\ \ \ \ \ \ \ \ \ \ \ \ \ 0.1\ \ \ \ \ \ \ \ \ \ \ \ \ \ .1x$
$20+x\ \ \ 0.35 \ \ \ \ (20+x)(.35)$
The amount of ethanol in the mixture is the sum of its two constituents: $20(.55)+.1x=(20+x)(.35)$