SOLUTION: The cooling system of a car has a capacity of 15 liters. If the system is currently fille with a mixture that is 40% antifreeze. How much of this mixture should be drained and repl

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Question 488231: The cooling system of a car has a capacity of 15 liters. If the system is currently fille with a mixture that is 40% antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that the system is filled with a solution that is 50% antifreeze?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = liters of mixture to be drained
and replaced with pure antifreeze
given:
+.4%2A15+=+6+ liters of antifreeze in the system at beginning
+.4x+ = liters of antifreeze that will be removed by draining
+6+-+.4x+ = liters of antifreeze left in system after draining
+6+-+.4x+%2B+x+ = liters of antifreeze left in system after draining
and replacing with pure antifreeze
------------
In words:
(liters of antifreeze after draining & replacing)/(total liters in system after draining) = 50%
+%28+6+%2B+.6x+%29+%2F+15+=+.5+
+6+%2B+.6x+=+.5%2A15+
+6+%2B+.6x+=+7.5+
+.6x+=+7.5+-+6+
+.6x+=+1.5+
+x+=+2.5+
2.5 liters need to be drained and replaced with pure antifreeze
check:
+15+-+2.5+=+12.5+ liters of system is 40% antifreeze
+.4%2A12.5+=+5+ liters antifreeze
+5+%2B+2.5+=+7.5+
+7.5+%2F+15+=+.5+
+7.5+=+7.5+
OK