SOLUTION: A silversmith has two alloys, one containing 50% silver and the other 40% silver. How much of each should be melted and combined to obtain 600 grams of an alloy containing 47% silv

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Question 1030324: A silversmith has two alloys, one containing 50% silver and the other 40% silver. How much of each should be melted and combined to obtain 600 grams of an alloy containing 47% silver?
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
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A silversmith has two alloys, one containing 50% silver and the other 40% silver.
How much of each should be melted and combined to obtain 600 grams of an alloy containing 47% silver?
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Take P grams of the 50% silver alloy and F grams of the 40% silver alloy.
Make sure that 

   P +    Q = 600,         (1)   and
0.5P + 0.4Q = 0.47*600.    (2) 

Solve this system for P and Q:

   P +    Q = 600,         (1)   and
0.5P + 0.4Q = 282.         (2)       ( 282 = 0.47*600 )

You can use any of substitution or eliminating method.

I think that if the teacher gave you such problem, you know how to solve the 2x2-system.

If not, look into the lessons 

    - Solution of the linear system of two equations in two unknowns by the Substitution method

    - Solution of the linear system of two equations in two unknowns by the Elimination method 

in this site.