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# Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three

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Math Expert
Joined: 02 Sep 2009
Posts: 51229
Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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07 Feb 2016, 09:35
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Difficulty:

65% (hard)

Question Stats:

58% (01:41) correct 42% (02:10) wrong based on 248 sessions

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Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

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Posts: 7108
Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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08 Feb 2016, 23:03
1
Bunuel wrote:
Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

Hi all,
these Qs are best done by weighted average method..

since we are asking of water in the end, lets concentrate on water only..
A solution has 2 quarts with fraction of water =2/3, almost 67%..
B solution has 3 quarts with fraction of water =3/8 almost 37%..
so the ratio A:B=2:3...
the average will therefore be closer to B % and will be 2/(2+3) of {67-37} away from B..
2/(2+3) of {67-37}= 2/5 * 30 =12..
so 37 +12 =49 nearly 50%
C
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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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12 Feb 2016, 17:45
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Hi All,

The design of this question gives you the opportunity to get to the solution by just doing arithmetic (although knowing your fraction-to-decimal conversions would help a great deal).

We're told that two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. We're asked APPROXIMATELY what percent of the combined five-quart mixture is water?

2/3 of 2 quarts = 4/3 quarts of water
3/8 of 3 quarts = 9/8 quarts of water

4/3 = 1.333
9/8 = 1.125

Total water = 1.333 + 1.125 = 2.458
Total quarts = 5

2.458/5 = a little less than 1/2 = a little less than 50%

The question you might be thinking at this point is "well, is it closer to 45% than it is to 50%?"

10% of 5 = .5
5% of 5 = .25

50% of 5 = 2.5
45% of 5 = 2.25

2.458 is closer to 2.5 than it is to 2.25, so...

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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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13 Feb 2016, 06:53
At first I got a little confused trying to think of how much and what a quart is - i.e. the quart is a unit of volume (for either the imperial or United States customary units) equal to a quarter of a gallon (hence the name quart), two pints, or four cups ...

So I decided to just think of this as a bucket of solution and use numbers to solve the problem. Since the fractions were 3'rds and 8'ths, I pick 24 as the total amount in each bucket.

Two quarts containing 2⁄3 water and 1⁄3 formula:
water = 2/3 * 24 * 2 = 16 *2 = 32

..are mixed with three quarts containing 3⁄8 water and 5⁄8 formula:

water = 3/8 * 24 * 3 = 9 * 3 = 27

... approximately what percent of the combined five-quart mixture is water:

32 + 27 / (24*5) = 59 / 120 =~ 60/120 = 50%
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Joined: 07 Dec 2014
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Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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25 May 2017, 10:12
1
Bunuel wrote:
Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

let x=% of water
2*2/3+3*3/8=5x
x≈50%
C
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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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31 May 2017, 18:03
Bunuel wrote:
Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

The first mixture contains 2 x 2/3 = 4/3 quarts of water, and the second mixture contains 3 x 3/8 = 9/8 quarts of water.

Thus, the percentage of the mixture that is water is (4/3 + 9/8)/5 = (32/24 + 27/24)/5 = (59/24)5 = 59/120 ≈ 0.49, so the closest answer is 50%.

Answer: C
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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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09 Jun 2017, 15:13
Bunuel wrote:
Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

1.(Quantity of solution 1 * proportion of element 1 + Quantity of solution 2 * proportion of element 1)/ (Quantity of solution 1 * Quantity of solution 2) = Quantity of water in mixture / Total Quantity

2. (2*( 2/3) + 3*(3/8) ) / 5 = 1/2 (approx) = 50%(approx)
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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three  [#permalink]

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05 Oct 2018, 22:19
Bunuel wrote:
Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

using mixture and alligation method:

$$\frac{(66.66-x)}{(x-37.5)}=\frac{2}{3}$$

$$200-3x=2x-75$$

$$5x=125$$

$$x=50$$

c is the correct answer
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Re: Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three &nbs [#permalink] 05 Oct 2018, 22:19
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# Two quarts containing 2 ⁄3 water and 1 ⁄3 formula are mixed with three

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