SOLUTION: Hi, I am having a problem setting up the correct equation for this problem. How much silver and lead should be added to 100 lbs of a mixture containing 15% silver and 30% lead to

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Question 138734: Hi, I am having a problem setting up the correct equation for this problem.
How much silver and lead should be added to 100 lbs of a mixture containing 15% silver and 30% lead to obtain an alloy containing 25% silver and 50% lead.
I believe the answer is 40lbs silver and 80lbs lead.
Thank you for your help.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How much silver and lead should be added to 100 lbs of a mixture containing 15% silver and 30% lead to obtain an alloy containing 25% silver and 50% lead.
I believe the answer is 40lbs silver and 80lbs lead.
---------------------------------
Start:
Amount = 100 lbs:
15% silver = 15 lbs
30% lead = 30 lbs
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Add:
silver = S
Lead = L
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End up with:
Amount: 100+S + L lbs
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EQUATIONS:
Silver: 15 + S = 0.25(100 + S + L)
15 + S = 25 + 0.25S + 0.25L
0.75S - 0.25L = 10
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Lead: 30 + L = 0.50(100+S+L)
30 + L = 50 + 0.50S + 0.50L
0.50S -0.50L = -20
--------------------------
Summary:
0.75S - 0.25L = 10
0.50S -0.50L = -20
--------------------
I used a Matrix method to get:
S = 40
L = 80
---------
You are correct.
Cheers,
Stan H.