Question 924971
Go straight to their question: "How much of the pure copper was used to make the new alloy?"


So they want to know how much pure copper to use. For now, we don't know it, so let's make


x = amount of pure copper (in kg)


We'll be adding x kg of pure copper


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We already have " 34 kg of a 12% copper alloy", so 34*0.12 = 4.08 kg of pure copper is already there.


We add x kg of pure copper to 4.08 kg to get x+4.08


In total, we have x+4.08 kg of pure copper.


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We are adding x kg of pure copper to be mixed with the 34 kg of copper alloy. So we'll have a total of x+34 copper alloy (copper + other stuff)


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Divide the two expressions to get


{{{(amount_pure_copper)/(amount_alloy) = (x+4.08)/(x+34)}}}


The expression must be set equal to 0.32 because we want the final alloy to be 32% copper.


{{{(x+4.08)/(x+34)=0.32}}}


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Solve for x.



{{{(x+4.08)/(x+34)=0.32}}}



{{{x+4.08=0.32(x+34)}}}



{{{x+4.08=0.32x+0.32*34}}}



{{{x+4.08=0.32x+10.88}}}



{{{x-0.32x=10.88-4.08}}}



{{{0.68x=6.8}}}



{{{x=6.8/0.68}}}



{{{x=10}}}



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Answer:



You must add <font size=5 color="red">10 kg</font> of pure copper.


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Let me know if that helps or not. Thanks.


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