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