SOLUTION: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed toget

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed toget      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 749228: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed together? I REALLY need help!!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of solution A needed
Let +b+ = liters of solution B needed
+.12a+ = liters of acid in solution A
+.04b+ = liters of acid in solution B
---------------------------------
(1) +a+%2B+b+=+60+
(2) +%28+.12a+%2B+.04b+%29+%2F+60+=+.1+
----------------------------
(2) +.12a+%2B+.04b+=+6+
(2) +12a+%2B+4b+=+600+
Multiply both sides of (1) by +4+ and
subtract (1) from (2)
-----------------
(2) +12a+%2B+4b+=+600+
(1) +-4a+-4b+=+-240+
+8a+=+360+
+a+=+45+
and, since
(1) +a+%2B+b+=+60+
(1) +45+%2B+b+=+60+
(1) +b+=+15+
45 liters of solution A are needed
15 liters of solution B are needed
check:
(2) +%28+.12a+%2B+.04b+%29+%2F+60+=+.1+
(2) +%28+.12%2A45+%2B+.04%2A15+%29+%2F+60+=+.1+
(2) +%28+5.4+%2B+.6+%29+%2F+60+=+.1+
(2) +6+=+.1%2A60+
(2) +6+=+6+
OK