SOLUTION: how many liters of a 10% alcohol solution must be mixed with 70 liters of a 80% solution to get a 60% solution? can you show me how to solve it as well as the answer please?

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Question 658364: how many liters of a 10% alcohol solution must be mixed with 70 liters of a 80% solution to get a 60% solution? can you show me how to solve it as well as the answer please?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = liters of 10% alcohol solution needed
+.1x+ = liters of alcohol in 10% solution
+.8%2A70+=+56+ liters of alcohol in 80% solution
given:
+%28+.1x+%2B+56+%29+%2F+%28+x+%2B+70+%29+=+.6+
+.1x+%2B+56+=+.6%2A%28+x+%2B+70+%29+
+.1x+%2B+56+=+.6x+%2B+42+
+.5x+=+14+
+x+=+14%2F.5+
+x+=+28++
28 liters of 10% alcohol solution are needed
check:
+%28+.1x+%2B+56+%29+%2F+%28+x+%2B+70+%29+=+.6+
+%28+.1%2A28+%2B+56+%29+%2F+%28+28+%2B+70+%29+=+.6+
+%28+2.8+%2B+56+%29+%2F+98+=+.6+
+58.8+%2F+98+=+.6+
+58.8+=+.6%2A98+
+58.8+=+58.8+
OK