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Bunuel
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How many ounces of water must be added to a 30-ounce solution that is Updated on: 10 Jul 2019, 23:59
Originally posted by Bunuel on 21 May 2017, 12:26.
Last edited by Sajjad1994 on 10 Jul 2019, 23:59, edited 1 time in total.
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83% (01:44) correct 17% (02:44) wrong based on 268 sessions

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How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18

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E
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How many ounces of water must be added to a 30-ounce solution that is 21 May 2017, 12:43
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30-ounce solution that is 40 percent alcohol = 30*0.4 =12 ounce alcohol

30-12 = 18 ounce water.

Backsolving method: Take the middle option C - 15

18+15 = 33 ounce water ; 12 ounce alcohol ;

12/45 = 4/15 which is greater than 25 %

Lets go to next greater option which is D - 16

18+16 = 34 ounce water ; 12 ounce alcohol ;

12/46 = 6/23 which is greater than 25 %

Lets go to next greater option which is E - 18

18+18 = 36 ounce water ; 12 ounce alcohol ;

12/48 = 1/4 which is 25 % .

Hence option E is the answer.
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How many ounces of water must be added to a 30-ounce solution that is 21 May 2017, 12:47
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12 / ( x +30) = 0.25, x = 18.
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How many ounces of water must be added to a 30-ounce solution that is 21 May 2017, 13:21
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Bunuel
How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18
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Let x = number of ounces of water to be added

(concentration of A)*(Volume of A) + (concentration of B to be added)*(Volume of B to be added)= (resultant concentration of new mixture)*(total volume of new mixture = A + B)

Water has an alcohol concentration of 0

(.40)*(30) + (0)(x) = (.25) (30 + x)

12 + 0x = 7.5 + .25x

4.5 = .25x

\(\frac{4.5}{.25}\) = 18 = x. Number of ounces of water to be added is
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(E) 18
Hope it helps
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How many ounces of water must be added to a 30-ounce solution that is 21 May 2017, 14:03
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Bunuel
How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18
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let x=ounces of water to be added
.6*30+x=.75(30+x)
x=18 ounces
E
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How many ounces of water must be added to a 30-ounce solution that is 28 May 2017, 11:56
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\(\frac{Total Alcohol}{total solution + added water} = \frac{1}{4}\)

\(\frac{12}{30+x} = \frac{1}{4} =>30+X = 12*4 => X = 48-30=18\)

Option: E

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How many ounces of water must be added to a 30-ounce solution that is 11 Mar 2018, 02:57
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Heseraj
\(\frac{Total Alcohol}{total solution + added water} = \frac{1}{4}\)

\(\frac{12}{30+x} = \frac{1}{4} =>30+X = 12*4 => X = 48-30=18\)

Option: E

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Nice Solution! Additional Approach yet simple as above

Alcohol before = Alcohol After
40% of 30 = 25% of (30+x)
40*30/25 = 30+x
48-30 = x = 18 = E
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How many ounces of water must be added to a 30-ounce solution that is 06 Nov 2024, 02:40
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