SOLUTION: An automobile cooling system currently has 20 quarts of a 35% antifreeze solution. The manufacturer recommends the systme be filled with a 50% antifreeze solution. How much of th

An automobile cooling system currently has 20 quarts of a 35% antifreeze
solution.  The manufacturer recommends the systme be filled with a 50%
antifreeze solution.  How much of the 35% soulution must be drained off so
that when replaced by pure antifreeze, the system contains the recommended 50%
solution?

Let x = amount to be drained off

After we drain off x quarts we have left 20-x quarts of 35% solution.

The number of quarts of pure antifreeze contained in the 20-x quarts that are
left in the radiator after draining is .35(20-x)

The number of quarts of pure antifreeze contained in the x quarts that we are
going to add is x quarts, because it is 100% antifreeze

The total number of quarts of pure antifreeze contained in the full radiator
after we add the x quarts of pure antifreeze is

.35(20-x) + x

Also the number of quarts of pure antifreeze that must be contained in the
full radiator after we add the pure antifreeze must be 50% of 20 or .50(20)
or 10 quarts

So .35(20-x) + x must equal 10

.35(20-x) + x = 10 

solve that and get x = 60/13 or 4 8/13 quarts

Edwin 
AnlytcPhil@aol.com