A brown flask contains a concoction that is 20% alcohol. A red flask contains a concoction with an unknown amount of alcohol. An equal amount of both flasks is poured into an empty jug. If the resulting mixture has an alcohol concentration that is 30% greater than the alcohol concentration of the brown flask, what percent alcohol did the red flask originally contain?

- anonymous

- chestercat

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- anonymous

good lord i am confused already. better take this one real slow

- anonymous

first off the alcohol concentration in the brown flask is 20% now we have to be careful about what the final alcohol concentration is, it is NOT 50%

- anonymous

unless they wrote the question carelessly
did you notice that they did not say how much of anything there was?

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## More answers

- anonymous

this is were you say "yes, i did notice that"

- anonymous

Its 26%

- anonymous

yes, 20% more than the original 20% is \(20\times 1.3=26\) for sure

- anonymous

now lets imagine there are 100 liters in each flask to make the numbers easy

- anonymous

I think it's 26% because the concertation is 30% greater than the brown=23% of alcohol. Then 23% is the average of the brown and the red, so it is 26% for the red flask.

- anonymous

i don't think so

- anonymous

Why exactly?

- anonymous

because when you are done, the total percent alcohol is 26%

- anonymous

so the red flask must have a higher concentration of alcohol than that
i find it easiest to work with numbers

- anonymous

I too confused right now xD

- anonymous

say each has 100 liters, the brown flask has 20 liters, of alcohol, the brown one unknown liters of alcohol (that is what we are trying to find)

- anonymous

when you mix them together, you have 200 liters total, and it is 26% alcohol
26% of 200 is 52 so there are 52 liters of alcohol total

- anonymous

20 liters came from the brown flask, the other 32 liters came from the red flask

- anonymous

This was way more complicated than I first thought xD

- anonymous

so the red flask had 32 liters or 32%

- anonymous

yeah i can see why it is confusing
first because they are using "percent' to mean two different things

- anonymous

crap sorry no one answered for so long i left my desk .

- anonymous

lol

- anonymous

let me read everything

- anonymous

welp

- anonymous

i can condense if if you like

- anonymous

so I know they had 26% but how do you find what's in the red flask?

- anonymous

let me show you an easy trick for these, if it was not clear from what i wrote

- anonymous

okay

- anonymous

you notice that they do not say how much each flask holds right?

- anonymous

yea

- anonymous

so it doesn't matter
if it doesn't matter, then you can pick a number, work with that number, and whatever answer you get will be right

- anonymous

okay

- anonymous

if you are working with percents, the easiest number to pick is 100

- anonymous

yea

- anonymous

so we say each has 100 liters ok?

- anonymous

yea

- anonymous

the brown one has 20% alcohol
that means it contains 20 liters of alcohol

- anonymous

yes

- anonymous

the red one has an unknown number of liters of alcohol, that is what we are trying to find

- anonymous

yea

- anonymous

mix them together, 100 liters + 100 liters is 200 liters

- anonymous

hmmmm okay

- anonymous

it is 26% alcohol and 26% of 200 is 52, so there are 52 liters of alcohol in the total 200 liters

- anonymous

hmmmm okay

- anonymous

20 of them came from the brown flask, so the remaining \(52-20=32\) liters came from the red flask

- anonymous

ouuuuuuuuuuuuu i see

- anonymous

that means the red flask had 32 liters of its 100 liters as alcholol

- anonymous

and 32 is 32% of 100
done

- anonymous

nice thanks Satellite!!!!

- anonymous

yw always happy to assist you

- anonymous

btw where did you find this problem?

- anonymous

I needed more practice for mixture problems so i googled it

- anonymous

couldn't find it on google

- anonymous

iono i just came across it

- anonymous

Cool

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