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A machine that produces silicon bottle stoppers, makes 36 stoppers wei

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A machine that produces silicon bottle stoppers, makes 36 stoppers wei  [#permalink]

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New post 18 Oct 2016, 01:30
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A machine that produces silicon bottle stoppers, makes 36 stoppers weighing 6y grams each, and 9x stoppers weighing 12 grams each. What is the average weight (arithmetic mean) per stopper?

A. (36y + 18x)/(y + 2)
B. (18y + 9x)/4
C. (36x)/(2y + 3x)
D. (24y + 12x)/(4 + x)
E. 6 + 3y

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Re: A machine that produces silicon bottle stoppers, makes 36 stoppers wei  [#permalink]

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New post 18 Oct 2016, 03:21
The total number silicon stoppers weighing 6y grams is 36 and 12 grams is 9x

Average weight = (36*6y + 9x*12)/36+9x
= (9(24x + 12y))/(9(4+x))
= 24x+12y/4+x (Option D)
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Re: A machine that produces silicon bottle stoppers, makes 36 stoppers wei  [#permalink]

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New post 18 Oct 2016, 05:12
Bunuel wrote:
A machine that produces silicon bottle stoppers, makes 36 stoppers weighing 6y grams each, and 9x stoppers weighing 12 grams each. What is the average weight (arithmetic mean) per stopper?

A. (36y + 18x)/(y + 2)
B. (18y + 9x)/4
C. (36x)/(2y + 3x)
D. (24y + 12x)/(4 + x)
E. 6 + 3y


36 stoppers weighing 6y grams each and 9x stoppers weighing 12 grams each

i.e. Total Weight = 36*6y + 9x*12 = 216y + 108x
Total No. of stoppers = 36 + 9x

average weight (arithmetic mean) per stopper = Total Weight / Total No. of Stoppers = (216y + 108x) / (36 + 9x)
average weight (arithmetic mean) per stopper = 9 (24y + 12x) / 9(4 + x) = (24y + 12x) / (4 + x)

Answer: Option D
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Re: A machine that produces silicon bottle stoppers, makes 36 stoppers wei  [#permalink]

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New post 18 Oct 2016, 06:32
Bunuel wrote:
A machine that produces silicon bottle stoppers, makes 36 stoppers weighing 6y grams each, and 9x stoppers weighing 12 grams each. What is the average weight (arithmetic mean) per stopper?

A. (36y + 18x)/(y + 2)
B. (18y + 9x)/4
C. (36x)/(2y + 3x)
D. (24y + 12x)/(4 + x)
E. 6 + 3y


\(\frac{(36*6y + 9x*12)}{( 36 + 9x)}\)

\(= \frac{9(4*6y + x*12)}{9(4 + x)}\)

\(= \frac{(4*6y + x*12)}{(4 + x)}\)

\(= \frac{(24y + 12x)}{(4 + x)}\)

Hence answer will be D. \(\frac{(24y + 12x)}{(4 + x)}\)
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Re: A machine that produces silicon bottle stoppers, makes 36 stoppers wei  [#permalink]

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Re: A machine that produces silicon bottle stoppers, makes 36 stoppers wei   [#permalink] 16 Oct 2018, 09:59
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