SOLUTION: the cooling system of car has a capacity of 15 liters. If the system is currently filled with a mixture that is 40% anitfreeze, how much if this mixture should be drained and repla

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Question 703384: the cooling system of car has a capacity of 15 liters. If the system is currently filled with a mixture that is 40% anitfreeze, how much if this mixture should be drained and replaced with pure anitfreeze so that the system is filled with a solution this is 50% antifreeze?
Found 2 solutions by nshah11, josmiceli:
Answer by nshah11(47) About Me  (Show Source):
You can put this solution on YOUR website!
Assume x liters of the mixture should be drained. The x liters consists of 0.40(x) antifreeze.
Remaining antifreeze after x liters are drained = 15(0.4) - 0.4(x)
Assume x liters of pure antifreeze is added. If so, then total antifreeze = 6 - 0.4(x) + x = 6 + 0.6(x)
(6 + 0.6(x))/(15) = 1/2
12 + 1.2x = 15
x = 2.5 liters

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
At the start,
+.4%2A15+=+6+ liters of pure antifreeze in 40% mixture
+4x+ = liters of pure antifreeze in mixture drained
--------------
+%28+6+-+.4x+%2B+x+%29+%2F+15+=+.5+
+%28+6+%2B+.6x+%29+%2F+15+=+.5+
+6+%2B+.6x+=+.5%2A15+
+.6x+=+7.5+-+6+
+.6x+=+1.5+
+x+=+1.5+%2F+.6+
+x+=+2.5+
2.5 liters of mixture must be drained
and replaced with pure antifreeze
--------------
check:
+%28+6+-+.4%2A2.5+%2B+2.5+%29+%2F+15+=+.5+
+%28+8.5+-+1+%29+%2F+15+=+.5+
+7.5+=+.5%2A15+
+7.5+=+7.5+
OK