SOLUTION: An alloy of metals is 25% copper. Another alloy is 50% copper. How much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: An alloy of metals is 25% copper. Another alloy is 50% copper. How much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 940860: An alloy of metals is 25% copper. Another alloy is 50% copper. How much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a+ = grams of 25% alloy needed
Let +b+ = grams of 50% alloy needed
+.25a+ = grams of copper in 25% alloy
+.5b+ = grams of copper in 50% alloy
-------------------------------------
(1) +a+%2Bb+=+1000+
(2) +%28+.25a+%2B+.5b+%29+%2F+1000+=+.45+
--------------------------------
(2) +.25a+%2B+.5b+=+450+
(2) +25a+%2B+50b+=+45000+
Multiply both sides of (1) by +25+
and subtract (1) from (2)
(2) +25a+%2B+50b+=+45000+
(1) +-25a+-+25b++=+-25000+
------------------------------
+25b+=+20000+
+b+=+800+
and, since
(1) +a+%2Bb+=+1000+
(1) +a+=+200+
---------------------
200 grams of 25% alloy are needed
800 grams of 50% alloy are needed
--------------------------------
check:
(2) +%28+.25%2A200+%2B+.5%2A800+%29+%2F+1000+=+.45+
(2) +%28+50+%2B+400+%29+%2F+1000+=+.45+
(2) +450+=+.45%2A1000+
(2) +450+=+450+
OK