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By weight, liquid A makes up 8 percent of solution R and 18 percent of

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By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 15 Jul 2018, 07:39
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A
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Question Stats:

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By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution?

A. 10%
B. 13%
C. 15%
D. 19%
E. 26%
Spoiler: OA

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By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 15 Jul 2018, 08:08
5 of liquid A in final solution
Bunuel wrote:
By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution?

A. 10%
B. 13%
C. 15%
D. 19%
E. 26%


let x=% of liquid A in final solution
.08*3+.18*7=10x
x=.15=15%
C
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Re: By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 19 Jul 2018, 06:22
Bunuel wrote:
By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution?

A. 10%
B. 13%
C. 15%
D. 19%
E. 26%


Weighted Avg. method :

Let us say liquid A accounts for x% weight of the final solution

\(\frac{3}{7} = \frac{18 - x}{x - 8}\)

\(10x = 150\)

\(x = 15%\)

(C)
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Re: By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 19 Jul 2018, 06:29
1
total solution = 3+7 =10
total weight of A = 3*8% + 7* 18% = 1.5
% of solution A = 1.5/10 *100 = 15%
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By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 19 Jul 2018, 07:25
\(\frac{(3×8 + 7×18)}{(3 + 7)}\) = \(\frac{150}{10}\) = 15 (C)
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Re: By weight, liquid A makes up 8 percent of solution R and 18 percent of  [#permalink]

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New post 29 Jul 2018, 06:31
Since the question asks for the weight of the Liquid A, we should find the availability of Liquid A in the mixture. Logically the percentage does not change even when the gram raises.
8% of Liquid A in the 3 gram of R = 0.08*3=0.24
18% of Liquid A in the 7 gram of S = 0.18*7=1.62
Now we should turn this into part/total form.
1.5/10*100=15%
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