SOLUTION: I need help with this!!! Here is the question. The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional pa

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Question 137341: I need help with this!!! Here is the question.
The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus, 18 karat gold is 18/24, or 75% pure gold; 12 karat gold is 12/24, or 50% pure gold, and so on. How much 12 karat gold should be mixed with pure gold to obtain 60 grams of 16 karat gold?
If I could please get some help on this! Thank you very much!
Found 2 solutions by vleith, stanbon:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
How much gold is in 60g of 16k gold?
gold+=+60%2A%2816%2F24%29 = 40g
Now set up an equation to solve for pure gold + 12k gold.
We know we have 60 grams total weight and 40g of gold.
Let X be the amount of pure gold in the mixture, then the amount of 12k gold is 60-X
gold+Content+=+%28Pure+gold+%2A+X%29+%2B+12kGold%2A%2860-X%29+
40+=+%2824%2F24%29+%2A+X+%2B+%2812%2F24%29%2A%2860-X%29+
+40%2A24+=+24X+%2B+720+-+12X+
+960+-+720+=+12X+
+240+=+12+X+
+20+=+X+
So we need to mix 20g of pure gold with 40g of 12k gold to get 60g of 16k gold.
Check your answer
Does 40+=+20+%2B+40%2A%280.50%29???

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The purity of gold is measured in karats, with pure gold being 24 karats.
Other purities of gold are expressed as proportional parts of pure gold.
Thus, 18 karat gold is 18/24, or 75% pure gold;
12 karat gold is 12/24, or 50% pure gold, and so on.
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How much 12 karat gold should be mixed with pure gold to obtain 60 grams of 16 karat gold?
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Pure gold DATA:
Amt. = x oz ; Amt of gold = x oz
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12 karat gold DATA:
Amt = 60-x oz; Amt of gold = 0.50(60-x) = 30 -0.5x oz
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16 karat Mixture DATA:
Amt = 60 oz; Amt. of gold = 16/24(60) = (2/3)(60) = 40 oz
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EQUATION:
gold + gold = gold
x + 30-0.5x = 40
0.5x = 10
x = 20 oz (Amount of pure gold in the mixture)
60-x = 40 oz (Amount of 12 karat gold needed for the mixture)
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Cheers,
Stan H.