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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.