SOLUTION: A car has a 15 quart capacity. There are 12 quarts with 30% antifreeze solution. How many quarts of pure antifreeze will you need to strengthen the solution to 40%? Please help!

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Question 632472: A car has a 15 quart capacity. There are 12 quarts with 30% antifreeze solution. How many quarts of pure antifreeze will you need to strengthen the solution to 40%?
Please help! Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = quarts of pure antifreeze needed
+.3%2A12+=+3.6+ quarts of pure antifreeze in 30% solution
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+%28+x+%2B+3.6+%29+%2F+%28+x+%2B+12+%29+=+.4+
+x+%2B+3.6+=+.4%2A%28+x+%2B+12+%29+
+x+%2B+3.6+=+.4x+%2B+4.8+
+.6x+=+1.2+
+x+=+2+
2 quarts of pure antifreeze are needed
check:
+%28+2+%2B+3.6+%29+%2F+%28+2+%2B+12+%29+=+.4+
+5.6%2F14+=+.4+
+5.6+=+.4%2A14+
+5.6+=+5.6+
OK
and since +12+%2B+2+ is les than 15, the capacity
is not exceeded