anonymous one year ago 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?

1. anonymous

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

2. 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%

3. anonymous

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

4. anonymous

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

5. anonymous

Its 26%

6. anonymous

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

7. anonymous

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

8. 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.

9. anonymous

i don't think so

10. anonymous

Why exactly?

11. anonymous

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

12. anonymous

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

13. anonymous

I too confused right now xD

14. 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)

15. 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

16. anonymous

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

17. anonymous

This was way more complicated than I first thought xD

18. anonymous

19. anonymous

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

20. anonymous

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

21. anonymous

lol

22. anonymous

23. anonymous

welp

24. anonymous

i can condense if if you like

25. anonymous

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

26. anonymous

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

27. anonymous

okay

28. anonymous

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

29. anonymous

yea

30. 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

31. anonymous

okay

32. anonymous

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

33. anonymous

yea

34. anonymous

so we say each has 100 liters ok?

35. anonymous

yea

36. anonymous

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

37. anonymous

yes

38. anonymous

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

39. anonymous

yea

40. anonymous

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

41. anonymous

hmmmm okay

42. anonymous

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

43. anonymous

hmmmm okay

44. anonymous

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

45. anonymous

ouuuuuuuuuuuuu i see

46. anonymous

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

47. anonymous

and 32 is 32% of 100 done

48. anonymous

nice thanks Satellite!!!!

49. anonymous

yw always happy to assist you

50. anonymous

btw where did you find this problem?

51. anonymous

I needed more practice for mixture problems so i googled it

52. anonymous

53. anonymous

iono i just came across it

54. anonymous

Cool