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A ten-gram piece of a certain alloy contains only gold and silver. If

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grinenkiv
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A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  23 Apr 2019, 16:25
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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
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MahmoudFawzy
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  23 Apr 2019, 21:29
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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
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A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  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
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  24 Apr 2019, 20:26
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grinenkiv wrote:
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


Current Composition : 10Grams = 7Gold + 3Silver

Future If 3G of S is 10% then total must be 30Grams => the rest 27G is Gold

We already have 7Grams of gold, So 27-7 = 20G of gold must be added to piece
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  24 Aug 2019, 05:40
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grinenkiv wrote:
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


Let x = the number of grams of gold that must be added to the piece so that the resulting piece is 10 percent silver. We can create the equation:

3/(10 + x) = 1/10

10 + x = 30

x = 20

Alternate Solution:

As the number of grams of silver in the alloy after the addition of gold does not change, the resulting alloy will contain 3 grams of silver as well. If the resulting piece is 10% silver, then the resulting piece must weigh 30 grams (so that 10% of it is 3 grams). Since the original piece was 10 grams, 30 - 10 = 20 grams of gold must be added.

Answer: D
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BrentGMATPrepNow
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  24 Aug 2019, 07:25
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grinenkiv wrote:
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


GIVEN: The piece weighs 10 grams. The piece contains 3 grams of silver, which means the remaining 7 grams are gold
Let x = the number of EXTRA grams of gold needed for the piece to be 10 percent silver.
With the addition of x grams of gold, the NEW weight of the piece = 10 + x

How many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?
We want: (grams of silver)/(TOTAL weight of piece) = 10%
Fill in values to get: 3/(10 + x) = 1/10 (aka 10%)
Cross multiply to get: (1)(10 + x) = (3)(10)
Simplify to get: 10 + x = 30
Solve: x = 20

Answer: D

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Brent
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  24 Aug 2019, 12:04
grinenkiv wrote:
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


let x=grams of gold to be added
7+x=.9(10+x)→
x=20 grams
D
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gvij2017
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  24 Aug 2019, 18:31
I did the problem this way.
Initially gold is 70% and silver is 30% in mix.
Now I add x gram of 100% pure gold to make final mix 10% of silver and the remaining 90% of gold.
By using alligation method:
70%............100%
...........90%.....
10/20= 7/x
x=14

Please tell me where I am wrong!
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Re: A ten-gram piece of a certain alloy contains only gold and silver. If [#permalink] New post  18 Jul 2022, 08:24
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