SOLUTION: Hello, I was wondering if you could help me with this math problem. The question is "Pure copper was mixed with 34 kg of a 12% copper alloy to produce a new alloy that is 32% coppe

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Question 924971: Hello, I was wondering if you could help me with this math problem. The question is "Pure copper was mixed with 34 kg of a 12% copper alloy to produce a new alloy that is 32% copper. How much of the pure copper was used to make the new alloy?"
I tried to work the problem out with an equation, but I could not get the correct equation.
Anything would help. I am so lost.
Thanks!
Found 2 solutions by ptaylor, jim_thompson5910:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Sure
Let x=amount of pure copper needed
Now we know that the amount of pure copper that exists before the mixture takes place (x+0.12*34) has to equal the amount of pure copper that exists after the mixture takes place (0.32*(34+x)). Soooo our equation to solve is:
x+0.12*34=0.32(34+x)
You solve
Hope this helps---ptaylor

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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

%28amount_pure_copper%29%2F%28amount_alloy%29+=+%28x%2B4.08%29%2F%28x%2B34%29

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

%28x%2B4.08%29%2F%28x%2B34%29=0.32

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Solve for x.


%28x%2B4.08%29%2F%28x%2B34%29=0.32


x%2B4.08=0.32%28x%2B34%29


x%2B4.08=0.32x%2B0.32%2A34


x%2B4.08=0.32x%2B10.88


x-0.32x=10.88-4.08


0.68x=6.8


x=6.8%2F0.68


x=10


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Answer:


You must add 10 kg of pure copper.

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Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

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