SOLUTION: Two copper-nickel alloys are to be mixed to obtain 12.00 kg of an alloy that contains 38.0% copper. How much of each alloy is needed if one alloy contains 22.0% and the other conta

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Two copper-nickel alloys are to be mixed to obtain 12.00 kg of an alloy that contains 38.0% copper. How much of each alloy is needed if one alloy contains 22.0% and the other conta      Log On


   



Question 992390: Two copper-nickel alloys are to be mixed to obtain 12.00 kg of an alloy that contains 38.0% copper. How much of each alloy is needed if one alloy contains 22.0% and the other contains 49.0% copper?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kg of 22% copper alloy
Let +b+ = kg of 49% copper alloy
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(1) +a+%2B+b+=+12+
(2) +%28+.22a+%2B+.49b+%29+%2F+12+=+.38+
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(2) +.22a+%2B+.49b+=+.38%2A12+
(2) +.22a+%2B+.49b+=+4.56+
(2) +22a+%2B+49b+=+456+
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Multiply both sides of (1) by 22 and
subtract (1) from (2)
(2) +22a+%2B+49b+=+456+
(1) +-22a+-+22b+=+-264+
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+27b+=+192+
+b+=+7.111+
and
(1) +a+%2B7.111+=+12+
(1) +a+=+4.888+
4.889 kg of 22% copper alloy is needed
7.111 kg of 49% copper alloy is needed
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check:
(2) +%28+.22a+%2B+.49b+%29+%2F+12+=+.38+
(2) +%28+.22%2A4.889+%2B+.49%2A7.111+%29+%2F+12+=+.38+
(2) +%28+1.07558+%2B+3.48439+%29+%2F+12+=+.38+
(2) +4.55997+=+.38%2A12+
(2) +4.55997+=+4.56+
close enough -OK