SOLUTION: A jeweler has 2 bars of gold alloy in stock, one of 12 carats and the other of 18 carats (24 carats is pure gold, 12 carats is 12/24 pure, ect.). How many grams of each alloy must
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Question 448973: A jeweler has 2 bars of gold alloy in stock, one of 12 carats and the other of 18 carats (24 carats is pure gold, 12 carats is 12/24 pure, ect.). How many grams of each alloy must be mixed to obtain 10 grams of 14 carat gold?
I know the equation is something like x + y = 10 and 12/24x + 18/24y =14/24(10) but thats as far as I can get.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A jeweler has 2 bars of gold alloy in stock, one of 12 carats and the other of 18 carats (24 carats is pure gold, 12 carats is 12/24 pure, ect.). How many grams of each alloy must be mixed to obtain 10 grams of 14 carat gold?
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I know the equation is something like
x + y = 10
12/24x + 18/24y =14/24(10)
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12x + 12y = 12*10
12x + 18y = 14*10
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subtract and solve for "y":
6y = 2*10
y = 3 1/3 grams (amt. of 18 carat gold needed)
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Solve for "x":
x + y = 10
x = 6 2/3 grams (amt. of 12 carat gold needed)
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Cheers,
Stan H.
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