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# a 30% solution of alcohol is mixed with a 50% solution of

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Director
Joined: 12 Jun 2006
Posts: 532
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a 30% solution of alcohol is mixed with a 50% solution of [#permalink]

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20 Sep 2007, 04:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1

Kudos [?]: 175 [0], given: 0

Re: what the %&*@ am i doing wrong? [Spoiler below red l [#permalink]

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20 Sep 2007, 04:41
ggarr wrote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100

It is actually quite simple. You want to find the ratio/weighted for each:

dunno if I can explain this well.. there were these 'killer' notes that killersquirrel provided some time ago

30% + 50 % = 45% of a 10 liter solution
ratio of 30% : 50% ---> 1 : 3
so 30% = 1/4 or 25% of 10L solution = 2.5L
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

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20 Sep 2007, 04:50
beckee,

yeah. thanks. I have the notes. I'm just trying to solve the old fashioned way. i'd like to understand the traditional methods before moving on to the shortcuts

can anyone tell me what I'm doing wrong?
Quote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1

Kudos [?]: 175 [0], given: 0

### Show Tags

20 Sep 2007, 04:56
ggarr wrote:
beckee,

yeah. thanks. I have the notes. I'm just trying to solve the old fashioned way. i'd like to understand the traditional methods before moving on to the shortcuts

can anyone tell me what I'm doing wrong?
Quote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100

I think you were getting there..but you have to set up simultaneous eqns. I would do it this way:

x + y = 10, or y = 10 - x

30x + 50 y = 45 (x + y)
30x + 50 (10-x) = 45 (10)
30x + 500 - 50x = 450
-20x = -50
20x = 50 -> 50/20
x = 2.5

see... still works out the old fashioned algebra way!
Intern
Joined: 11 Sep 2007
Posts: 11
Followers: 1

Kudos [?]: 0 [0], given: 0

Re: what the %&*@ am i doing wrong? [Spoiler below red l [#permalink]

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20 Sep 2007, 11:11
beckee529 wrote:
ggarr wrote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100

It is actually quite simple. You want to find the ratio/weighted for each:

dunno if I can explain this well.. there were these 'killer' notes that killersquirrel provided some time ago

30% + 50 % = 45% of a 10 liter solution
ratio of 30% : 50% ---> 1 : 3 so 30% = 1/4 or 25% of 10L solution = 2.5L

This intrigues me - I don't understand the ratio of 1:3. Can anyone provide a link to the killer notes? I'd like to learn this.
Manager
Joined: 17 May 2007
Posts: 72
Followers: 2

Kudos [?]: 29 [0], given: 0

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20 Sep 2007, 11:20
someone had posted this file and i found it extremely helpful...took me all of 5 seconds to solve the problem
Attachments

File comment: mixture problems made easy

CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 11

Kudos [?]: 851 [0], given: 4

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17 Oct 2007, 11:35
beckee529 wrote:
ggarr wrote:
beckee,

yeah. thanks. I have the notes. I'm just trying to solve the old fashioned way. i'd like to understand the traditional methods before moving on to the shortcuts

can anyone tell me what I'm doing wrong?
Quote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

__________________________________________________________

I'm doing this and coming up empty.
30(L)/100 + 50(10-L)/100 = (10)45/100

I think you were getting there..but you have to set up simultaneous eqns. I would do it this way:

x + y = 10, or y = 10 - x

30x + 50 y = 45 (x + y)
30x + 50 (10-x) = 45 (10)
30x + 500 - 50x = 450
-20x = -50
20x = 50 -> 50/20
x = 2.5

see... still works out the old fashioned algebra way!

i like this way better. more intuitive
Director
Joined: 03 May 2007
Posts: 886
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 190 [0], given: 7

Re: what the %&*@ am i doing wrong? [Spoiler below red l [#permalink]

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17 Oct 2007, 16:04
ggarr wrote:
a 30% solution of alcohol is mixed with a 50% solution of alcohol to form a 10 liter solution of 45% alchohol. How much of the 30% solution was used.

2.0 liters
2.5 liters
2.7 liters
3.0 liters
3.2 liters

B. o.3x + 0.5 (1-x) = .45
x = 25%

so 30% alchohal has 25% of 10 lt = 2.5 lt.
VP
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 103 [0], given: 0

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17 Oct 2007, 18:19
gowani wrote:
someone had posted this file and i found it extremely helpful...took me all of 5 seconds to solve the problem

Appreciate gowani,
it will take me now 3 seconds to solve this kinda PS!
17 Oct 2007, 18:19
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