Question

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?

Answer 1

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

Answer 2

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%

Answer 3

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

Answer 4

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

Answer 5

Its 26%

Answer 6

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

Answer 7

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

Answer 8

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.

Answer 9

i don't think so

Answer 10

Why exactly?

Answer 11

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

Answer 12

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

Answer 13

I too confused right now xD

Answer 14

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)

Answer 15

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

Answer 16

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

Answer 17

This was way more complicated than I first thought xD

Answer 18

so the red flask had 32 liters or 32%

Answer 19

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

Answer 20

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

Answer 21

lol

Answer 22

let me read everything

Answer 23

welp

Answer 24

i can condense if if you like

Answer 25

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

Answer 26

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

Answer 27

okay

Answer 28

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

Answer 29

yea

Answer 30

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

Answer 31

okay

Answer 32

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

Answer 33

yea

Answer 34

so we say each has 100 liters ok?

Answer 35

yea

Answer 36

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

Answer 37

yes

Answer 38

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

Answer 39

yea

Answer 40

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

Answer 41

hmmmm okay

Answer 42

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

Answer 43

hmmmm okay

Answer 44

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

Answer 45

ouuuuuuuuuuuuu i see

Answer 46

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

Answer 47

and 32 is 32% of 100
done

Answer 48

nice thanks Satellite!!!!

Answer 49

yw always happy to assist you

Answer 50

btw where did you find this problem?

Answer 51

I needed more practice for mixture problems so i googled it

Answer 52

couldn't find it on google

Answer 53

iono i just came across it

Answer 54

Cool