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A factory cleans its machinery with a solution that is 87% water and

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A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 22 Jun 2017, 23:01
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A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres

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Re: A Factory Cleans its machinery with  [#permalink]

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New post 22 Jun 2017, 23:16
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akshayk wrote:
A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres


Vinegar content in Ideal Solution should be - 13%
Vinegar content is given solution - 260 x 40%
Total volume of the solution = 260 x 40 x 100/13 = 800
Water that need to be added = 800-260 = 540

Answer D
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A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 23 Jun 2017, 09:04
akshayk wrote:
A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres

We have a solution that is 40% vinegar. We need to add water, which is 0% vinegar, to obtain a resultant solution that is 13% vinegar.

Let A = solution with 40% vinegar

Let w = amount of water to be added

A + w = Total volume of resultant mixture

Water is 0% vinegar.

(Concen. of A)(Vol of A) + (Concen. of w)(Vol of w) = (Desired concen. of resultant solution)(Vol of resultant solution)

.40(A) + (0)w = .13(A + w)

.40(240) + 0w = .13(240 + w)

104 + (0)w = (.13)(240) + .13w

104 = 33.8 + .13w

70.2 = .13w

7020 = 13W

w = 540

Answer D
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 23 Jun 2017, 10:57
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akshayk wrote:
A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres


let w=water to be added
.6*260+w=.87(260+w)
w=540 liters
D
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 12 Jul 2017, 09:27
Can someone help me with this question? I am unable to understand the solutions provided. Thanks
p.s: Is this a mixture problem?
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 12 Jul 2017, 10:19
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Let \(x\) be the amount of water to be added to the solution.

The 260 litre solution contains 60% water, so \(\frac{260*60}{100} = 156\)

\(\frac{156+x}{260+x} = \frac{87}{100}\)

\(15600 + 100x = 22620 + 87x\)

\(13x = 7020\)

\(x = 540\). Ans - D.
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 12 Jul 2017, 10:39
From allegation- (40-13):(13-0)=X:260 on solving, X=540

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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 16 Jul 2017, 17:23
1
akshayk wrote:
A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres


We need the vinegar solution to be 13% vinegar.

We have 260 litres that contain 0.4(260) = 104 litres of vinegar.

We can let x = the number of litres of water to be added and create the following equation:

104/(260 + x) = 13/100

10,400 = 13(260 + x)


10,400 = 3,380 + 13x

7,020 = 13x

540 = x

Answer: D
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A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post Updated on: 18 Jul 2017, 20:21
Another way to look at the problem:

Initial Solution:

Volume of water = 260 *60/100 = 156 litres ---(1)

The addition of water:

Let the volume of water to be added = x litres ---(2)

Final Solution: (Given in the problem)

Volume of water in the final solution = 87% = 87/100

We can represent the percentage of water in the final solutions as:

(156 + x)/(260+x) = 87/100

15600 + 100x = 87*260 +87x
15600 - 22620 = 87x - 100x
- 7020 = -13x
x = 540
Attachments

mixtureproblem.jpg
mixtureproblem.jpg [ 18.32 KiB | Viewed 1432 times ]


Originally posted by gary391 on 18 Jul 2017, 18:00.
Last edited by gary391 on 18 Jul 2017, 20:21, edited 1 time in total.
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A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 18 Jul 2017, 18:06
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Alligation approach:
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File comment: Alligation Approach:
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 19 Jul 2017, 05:03
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[quote="Blackbox"]Can someone help me with this question? I am unable to understand the solutions provided. Thanks
p.s: Is this a mixture problem?

hi. let me try to explain. to have optimal proportion of mixture with two liquids: water must be 87% of the total solution, while vinegar must be 13% of the total solution. we have total solution which is 260 liters. 40 % of 260 = 104 is vinegar. the rest is water (260-104 = 156) now we are asked how much more water do we need to have 13 % of vinegar and 87 % of water. now we can use simple proportional method :) 13/87 = 104/x cross multiply and x = 696. since 156 liters of water is already there we need to subtract 696-156 = 540 YAY ! :-D here is answer!!

is it clear :)?

have a great day :)
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Re: A factory cleans its machinery with a solution that is 87% water and  [#permalink]

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New post 21 Jul 2017, 22:34
ScottTargetTestPrep wrote:
akshayk wrote:
A factory cleans its machinery with a solution that is 87% water and the remainder vinegar. If the factory manager starts with 260 Litres of a 40% vinegar solution, how much water must the manager add to the existing solution to attain the proper vinegar concentration for cleaning the machinery?

A) 104 Litres
B) 120 Litres
C) 470 Litres
D) 540 Litres
E) 800 Litres


We need the vinegar solution to be 13% vinegar.

We have 260 litres that contain 0.4(260) = 104 litres of vinegar.

We can let x = the number of litres of water to be added and create the following equation:

104/(260 + x) = 13/100

10,400 = 13(260 + x)


10,400 = 3,380 + 13x

7,020 = 13x

540 = x

Answer: D


Can you please explain how did you form this equation?
104/(260 + x) = 13/100
Thanks
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Re: A factory cleans its machinery with a solution that is 87% water and   [#permalink] 21 Jul 2017, 22:34
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