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Manager  Joined: 14 Dec 2004
Posts: 100
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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17 00:00

Difficulty:   35% (medium)

Question Stats: 72% (02:19) correct 28% (02:44) wrong based on 452 sessions

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Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

Originally posted by cloaked_vessel on 04 Apr 2005, 11:04.
Last edited by Bunuel on 27 Jun 2015, 06:22, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Joined: 02 Sep 2009
Posts: 59588
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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8
4
arshu27 wrote:
cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

"Bunuel,

can you please explain the solution stepwise as i have no idea as to how to start this sort of mixture questions. Thanks!

Approach #1:

Minum contains 5 percent hydrogen peroxide.
Maxim contains 20 percent hydrogen peroxide.

Minum:Maxim = (20 - 15):(15 - 5) = 1:2. (Check for more here: http://www.veritasprep.com/blog/2011/04 ... -mixtures/)

So, for the final concentration to be 15% for every par of Minum we should take 2 parts of Maxim. Since, we are mixing 3 parts of Minum, we should take 3*2 = 6 parts of Maxim.

Approach #2:

Equate hydrogen peroxide:

5% of 3 parts + 20% of x parts = 15% of total, so 15% of 3 + x parts:
0.05*3 + 0.2*x = 0.15(3 + x)
x = 6.

Another approach would be just to plug in the answers and work backwards.

Hope it helps.
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Senior Manager  Joined: 19 Feb 2005
Posts: 364
Location: Milan Italy
Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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say one quart is 100/3
you have 0.05*100=5
then backsolve
start from C -> 4.5*100/3=150
150*0.2=30
in the new mixture there are 35/250
we needed 37.5 (more)
now D
6*100/3=200
200*0.2=40
45/300
perfect
VP  Joined: 30 Sep 2004
Posts: 1149
Location: Germany
Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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1
3*0,05+0,2x=0,15(x+3) => x=6 => D!
Manager  Joined: 04 Mar 2005
Posts: 93
Location: NYC
Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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3
cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A) 3 quarts

B) 3.75 quarts

C) 4.5 quarts

D) 6 quarts

E) 9 quarts

Ans id 'D'
5% HydPer&Water (HPW) of 3 quart of Minum= .15 q
20% of HPW of x q of Maxim = .2x
Total = .15 + .2x = .15 (3+x)
Solving , x=6 quart
Intern  Joined: 22 Mar 2008
Posts: 38

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2
2
let 'x' be the qty of maxim which has to be mixed with minum.
so, the total qty of the mixture=(x+3).
Since the mixture has 15% of hydrogen peroxide
we can have the eqn as
(5%*3)+(20%*x)=15%*(x+3)
solving this we get x=6.

hence D.
Intern  Joined: 25 Jan 2014
Posts: 15
Concentration: Technology, General Management
Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

"Bunuel,

can you please explain the solution stepwise as i have no idea as to how to start this sort of mixture questions. Thanks!
Manager  Joined: 11 Sep 2013
Posts: 104
Re: A chemist has 3 liters of a bleaching chemical, Minum, which is compos  [#permalink]

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shyind wrote:
A chemist has 3 liters of a bleaching chemical, Minum, which is composed of 5 percent hydrogen peroxide. A different type of bleaching chemical, Maxim, which is composed of 20 percent hydrogen peroxide, will be mixed with three liters of Minum. How many liters of maxim should be added to the three liters of Minum so that the resulting mixture is 15 percent Hydrogen peroxide.

A. 3

B. 3.75

C. 4.5

D. 6

E. 9

x=the number of liters of Maxim

15(x+3) = 5*3 + 20x
=> x = 6

Ans: D
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A chemist has 3 liters of a bleaching chemical, Minum, which is compos  [#permalink]

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1
(1) The variables in the problem
$$m =$$ # liters of minum; $$cm =$$concentration (%) of minum
$$M =$$ # liters of Maxim; $$cM =$$concentration (%) of Maxim
$$T =$$ # liters in total after mixing both minum and Maxim; $$cT =$$concentration (%) of the mixture

(2) What we know from the stem
From the stem, we know that $$m=3, rm = 5, rM=20$$. $$M$$ is unknown.
$$T = m + M = 3 + M$$
What we want to know: $$M$$

(3)From all of thi above, we have that

$$\frac{m * cm + M * cM}{T} = cT$$

(4) Plugging in the values from (2):

$$\frac{3 * 5 + M * 20}{(3 + M)} = 15$$

If we solve for $$M$$ we get $$M=6$$, so is the correct answer.

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Posts: 1870
Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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We just need to equate the hydrogen peroxide here

5% of 3 + 20% of x = 15% of (x+3)
0.05*3 + 0.2*x = 0.15(3 + x)
0.15 + 0.2x = 0.45 +0.15x
0.05x = 0.3

x = 6 Option D
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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Minum contains 5% hydrogen peroxide, Maxim contains 20%.
Mixture contains 15%.

Applying ratio and mixture rule Minum and Maxim should be mixed in ratio (20-15):(15-5) or 5:10 or 1:2.

Minum is of 3 quarts. So Maxim should be of 6 quarts.
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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let x=liters of Maxim to be added
3*.05+x*.2=.15(3+x)
x=6 quarts
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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1
Minum contains 5 percent hydrogen peroxide.
Maxim contains 20 percent hydrogen peroxide.

Minum:Maxim = (20 - 15):(15 - 5) = 1:2. (Using Alligation)

So, since Minum is 3 quarts, Maxim will be 6 quarts!
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Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

Simplifying the arithmetic a bit by changing decimal percent concentrations to integers . . .

Let x = amount of Maxim to be added

5(3) + 20(x) = 15(3 + x)
15 + 20x = 45 + 15x
5x = 30
x = 6

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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

Using allegation :
Let x be the quantity of Maxim added
3/x=(20-15)/(15-5)
x=6
Ans. D
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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how do we backsolve this by using answer options?
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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cloaked_vessel wrote:
Three quarts of a bleaching chemical, Minum, contains 5 percent hydrogen peroxide and water. A different type of bleaching chemical, Maxim, which contains 20 percent hydrogen peroxide, will be mixed with the three quarts of Minum. How much of type Maxim should be added to the three quarts of Minum so that the resulting mixture contains 15 percent hydrogen peroxide?

A. 3 quarts
B. 3.75 quarts
C. 4.5 quarts
D. 6 quarts
E. 9 quarts

We can let the number of quarts of Maxim = y and create the following equations:

0.05(3) + 0.2y = 0.15(3 + y)

5(3) + 20y = 15(3 + y)

15 + 20y = 45 + 15y

5y = 30

y = 6

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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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Weighted avg method.
Formula
w1/w2=(a2-avg)/avg-a1)
a2=20
Avg=15
a1=5
plug in
w1/w2=(20-15)/(10-5)=1/2
w1=3
3/w2=1/2 0r w2=6.
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Re: Three quarts of a bleaching chemical, Minum, contains 5 percent hydrog  [#permalink]

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