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A ten-gram piece of a certain alloy contains only gold and silver. If
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23 Apr 2019, 16:25
23 Apr 2019, 16:25
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Difficulty:
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Question Stats:
78% (01:45) correct
22%
(01:43)
wrong
based on 264
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A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?
A. 30
B. 27
C. 25
D. 20
E. 17
A. 30
B. 27
C. 25
D. 20
E. 17
Re: A ten-gram piece of a certain alloy contains only gold and silver. If
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23 Apr 2019, 21:29
23 Apr 2019, 21:29
1
Kudos
The current alloy composition: Silver : Gold : Total = 3:7:10
To reduce the silver percent to 10, we will increase the gold percent to 90 (\(\frac{9}{10}\) of total).
let x be the gold amount to be added.
\(\frac{Gold + x}{Total + x} = \frac{7+x}{10+x} = \frac{9}{10}\)
\(70 + 10x = 90 + 9x\) ---> \(x = 20\) ... D
To reduce the silver percent to 10, we will increase the gold percent to 90 (\(\frac{9}{10}\) of total).
let x be the gold amount to be added.
\(\frac{Gold + x}{Total + x} = \frac{7+x}{10+x} = \frac{9}{10}\)
\(70 + 10x = 90 + 9x\) ---> \(x = 20\) ... D
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A ten-gram piece of a certain alloy contains only gold and silver. If
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23 Apr 2019, 21:49
23 Apr 2019, 21:49
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given total =10
and silver = 3gms
thus gold = 7 gms
now percent of silver = \((3/10)*100\) = 30% (this line was just to understand)
we have to make it 10%
so let the amount of gold added be g
therefore
\(\frac{3}{(10+g)} = \frac{10}{100}\)
solve the equation which gives g = 20
Hence answer D
and silver = 3gms
thus gold = 7 gms
now percent of silver = \((3/10)*100\) = 30% (this line was just to understand)
we have to make it 10%
so let the amount of gold added be g
therefore
\(\frac{3}{(10+g)} = \frac{10}{100}\)
solve the equation which gives g = 20
Hence answer D
