SOLUTION: 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?

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:
and

Check!

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