SOLUTION: ) Sally needs 10 lb of metal with 33 % silver. If Sally combines one metal with 18 % silver, and another with 73 % silver, how much of each metal does Sally need?

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Question 1126661: ) Sally needs 10 lb of metal with 33 % silver. If Sally combines
one metal with 18 % silver, and another with 73
% silver, how much of each metal does Sally need?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of 18% silver needed
Let +b+ = pounds of 73% silver needed
------------------------------------------------
(1) +a+%2B+b+=+10+
(2) +%28+.18a+%2B+.73b+%29+%2F+10+=+.33+
-----------------------------------------
(2) +.18a+%2B+.73b+=+3.3+
(2) +18a+%2B+73b+=+330+
Multiply both sides of (1) by +18+
and subtract (1) from (2)
(2) +18a+%2B+73b+=+330+
(1) +-18a+-+18b+=+-180+
------------------------------
+55b+=+150+
+b+=+2.727+
and
+a+%2B+2.727+=+10+
+a+=+7.273+
--------------------------
7.273 pounds of 18% silver
2.727 pounds of 73% silver
---------------------------------
check:
(2) +%28+.18a+%2B+.73b+%29+%2F+10+=+.33+
(2) +%28+.18%2A7.273+%2B+.73%2A2.727+%29+%2F+10+=+.33+
(2) +%28+1.309+%2B+1.991+%29+%2F+10+=+.33+
(2) +3.299+=+3.3+
error due to rounding off