Question 937620: Gold coin is usually 90% gold and 10% copper. How many ounces of pure gold (24K) must be added to 24 ounces of a 14 carat gold ring to make an alloy of gold coin? ( answer is 76 - show your solution )
Found 2 solutions by TimothyLamb, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = ounces of 24K gold (100% pure gold)
14K "gold alloy" contains 58.33% gold, the remaining weight is other metals (copper, etc.)
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express percents as decimals:
100% = 1.00
90% = 0.90
58.33% = 0.5833
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make an equation for the ounces of gold in each "input" metal, and in the "output" coin alloy:
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input metals:
1.0x = ounces of pure 24K gold
0.5833*24 = ounces of gold in 24 oz of 14K alloy
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output alloy:
0.90*(x + 24) = ounces of gold in the "output" coin alloy
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1.0x + 0.5833*24 = 0.90*(x + 24)
x + 0.5833*24 = 0.90x + 0.90*24
x - 0.90x = 0.90*24 - 0.5833*24
0.10x = 0.90*24 - 0.5833*24
x = (0.90*24 - 0.5833*24)/0.10
x = 76.008
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answer:
about 76 oz of 24K gold must be added
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Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Gold coin is usually 90% gold and 10% copper. How many ounces of pure gold (24K) must be added to 24 ounces of a 14 carat gold ring to make an alloy of gold coin? ( answer is 76 - show your solution )
Let amount of pure gold to mix, be G
Then we get: 14 + G = .9(G + 24)
14 + G = .9G + 21.6
G - .9G = 21.6 – 14
.1G = 7.6
F, or amount of gold =  , or  oz
You can do the check!!
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