Question 53078: The cooling system of a certain foreign-made car has a capacity of 16 liters. If the system is filled with a mixture that is 35% antifreeze, how much of this mixture should be drained and refilled by pure antifreeze so that the system is filled with a solution that is 50% antifreeze?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! I will solve this problem using two approaches to demonstrate, once again, the flexibility that is frequently available in solving mixture problems.
Let x=the amt of initial mixture that is drained and refilled with 100% antifreeze. Note: the initial mixture contains 35% antifreeze and 65%(water?).
First, we'll examine the water:
Amt of water in initial mixture (16)(.65)minus amt of water that was drained out (x)(.65) equals the amt of water in the final mixture (16)(.50). Our equation to solve is:
(16)(.65)-.65x=(16)(.50) simplifying, we have
10.4-.65x=8 and
-.65x=-2.4
x=3.69 liters
Now, lets examine the antifreeze:
Amt of antifreeze in the initial mixture(16)(.35)minus amt of antifreeze that was drained out (x)(.35) plus the pure antifreeze that was added back (x)(1) equals amt of antifreeze in the final mixture (16)(.50). Our equation to solve is:
(16)(.35)-.35x+x=(16)(.50) simplifying, we have
5.6+.65x=8 and
.65x=2.4
x=3.69 liters
Hope this helps -----ptaylor
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