Question 107664This question is from textbook beggining algebra
: 27. How much of an alloy that is 20% copper should be mixed with 200ounces of an alloy that is 50% copper in order to get an alloy of 30% copper?
This question is from textbook beggining algebra
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You want to know how much 20% copper alloy, so let that be x. We also don't know the total amount of 30% alloy, so let that be y.
Now, let's figure out what we do know.
The amount of 20% alloy plus the 200 oz. of 50% alloy must equal the amount of 30% alloy, so:
Eq 1) 
We also know that the amount of copper in the 20% alloy is 0.2x, the amount of copper in the 50% alloy is 50% of 200 oz, or 100 oz, and the amount of copper in the 30% alloy must be 0.3y. We also know that the copper in the 20% alloy plus the copper in the 50% alloy must equal the copper in the 30% alloy. Therefore:
Eq 2) 
Now it is a matter of solving two simultaneous linear equations in two variables. There are a number of methods, but this is the one I like. First re-arrange the equations to standard form,  . Or, in this case:
 and 
Then I multiply the 2nd equation by -5: 
Then add the result to the first equation, term by term: 
Then since 
 ounces.
Check:
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 Check!
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