SOLUTION: What weight of an alloy containing 10% silver must be melted with an alloy containing 60% silver to obtain 10 lb of an alloy containing 40% silver?

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Question 493024: What weight of an alloy containing 10% silver must be melted with an alloy containing 60% silver to obtain 10 lb of an
alloy containing 40% silver?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of 10% silver alloy to be added
Let b = pounds of 60% silver alloy to be added
given:
+.1a+ = pounds of silver in 10% alloy
+.6b+ = pounds of silver in 60% alloy
+.4%2A10+=+4+ = pounds of silver in final alloy
-------------------
(1) +a+%2B+b+=+10+
(2) +.1a+%2B+.6b+=+4+
----------------
(2) +a+%2B+6b+=+40+
Subtract (1) from (2)
(2) +a+%2B+6b+=+40+
(1) +-a+-+b+=+-10+
+5b+=+30+
+b+=+6+
and, since
(1) +a+%2B+b+=+10+
(1) +a+%2B+6+=+10+
(1) +a+=+4+
4 pounds of 10% silver alloy need to be added
6 pounds of 60% silver alloy need to be added
check answer:
(2) +.1a+%2B+.6b+=+4+
(2) +.1%2A4+%2B+.6%2A6+=+4+
(2) +.4+%2B+3.6+=+4+
(2) +4+=+4+
OK