SOLUTION: A silversmith has two alloys, one containing 70% silver and the other 20% silver. How much of each should be melted and combined to obtain 500 grams of an alloy containing 55% silv

Question 534086: A silversmith has two alloys, one containing 70% silver and the other 20% silver. How much of each should be melted and combined to obtain 500 grams of an alloy containing 55% silver?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let x be the amount (in grams) of the 70% alloy.
Let y be the amount (in grams) of the 20% alloy.
We want
and
or
Now we have a system of linear equations:
and

We can solve by elimination like this:
multiply the first equation times -0.2 to get

and add it to the second equation to eliminate y, getting
so
Plugging that value back into
we get
so
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