SOLUTION: Sam needs 3 lb of metal with 43% silver. If sam combines one metal with 18% silver, and another with 80% silvet, how much metal does he need?

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Question 991979: Sam needs 3 lb of metal with 43% silver. If sam combines one metal with 18% silver, and another with 80% silvet, how much metal does he 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 80% silver needed
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(1) +a+%2B+b+=+3+
(2) +%28+.18a+%2B+.8b+%29+%2F+3+=+.43+
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(2) +.18a+%2B+.8b+=+1.29+
(2) +18a+%2B+80b+=+129+
Multiply both sides of (1) by +18+
and subtract (1) from (2)
(2) +18a+%2B+80b+=+129+
(1) +-18a+-+18b+=+-54+
----------------------
+62b+=+75+
+b+=+1.21
and
(1) +a+%2B+b+=+3+
(1) +a+=+1.79+
1.79 pounds of 18% silver are needed
1.21 pounds of 80% silver are needed
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check:
(2) +%28+.18%2A1.79+%2B+.8%2A1.21+%29+%2F+3+=+.43+
(2) +%28+.3222+%2B+.968+%29+%2F+3+=+.43+
(2) +1.29+=+3%2A.43+
(2) +1.29+=+1.29+
OK