SOLUTION: You are making 10 tons of concrete that is 48.5% cement by mixing a 12% cement mixture with a 85% cement mixture. How much of the 85% cement mixture must you use? How much of the

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Question 533274: You are making 10 tons of concrete that is 48.5% cement by mixing a 12% cement mixture with a 85% cement mixture. How much of the 85% cement mixture must you use? How much of the 12% cement mixture must
you use

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = tons of 12% mixture needed
Let +b+ = tons of 85% mixture needed
given:
(1) +a+%2B+b+=+10+
(2) +%28+.12a+%2B+.85b+%29+%2F+10+=+.485+
----------------------------
(2) +.12a+%2B+.85b+=+10%2A.485+
(2) +.12a+%2B+.85b+=+4.85+
(2) +12a+%2B+85b+=+485+
Multiply both sides of (1) by +12+
and subtract (1) from (2)
(2) +12a+%2B+85b+=+485+
(1) +-12a+-+12b+=+-120+
+73b+=+365+
+b+=+5+
and, since
(1) +a+%2B+b+=+10+
(1) +a+=+10+-+5+
(1) +a+=+5+
5 tons of 12% mixture are needed
5 tons of 85% mixture are needed
check:
(2) +%28+.12%2A5+%2B+.85%2A5+%29+%2F+10+=+.485+
(2) +%28+.6+%2B+4.25+%29+%2F+10+=+.485+
(2) +4.85+%2F+10+=+.485+
(2) +4.85+=+4.85+
OK