SOLUTION: The capacity of a car radiator is 20 quarts. If it’s full of a 55% antifreeze solution, how many quarts must be drained off and replaced by an 80% solution to make 20 quarts of a 7

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Question 418175: The capacity of a car radiator is 20 quarts. If it’s full of a 55% antifreeze solution, how many quarts must be drained off and replaced by an 80% solution to make 20 quarts of a 70% solution.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = quarts that must be drained off
In words:
(quarts of antifreeze in final solution)/(quarts of final solution) = 70%
given:
quarts of antifreeze in radiator originally
= quarts of antifreeze in solution drained off
= quarts of antifreeze in solution left after
draining off quarts
= quarts of antifreeze in solution added
--------------





12 quarts must be drained off and 12 quarts of 80% solution
must be added
check answer:





OK
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The capacity of a car radiator is 20 quarts. If it’s full of a 55% antifreeze solution, how many quarts must be drained off and replaced by an 80% solution to make 20 quarts of a 70% solution?

1.  We drain off x quarts.
2.  There are now 20-x quarts of 55% antifreeze left in the radiator.
3.  The amount of pure antifreeze that's left in there is .55(20-x) qts.
4.  We will now replace the x quarts with x quarts of 80% antifreeze. 
5.  The pure alcohol in those x quarts we are replacing is .80x.
6.  So the total number of quarts of pure alcohol now is .55(20-x)+.80x qts.
5.  This number of quarts of pure alcohol in there now must equal 
    to 70% of 20 qts, or .70(20) qts 
6.  So the equation is:

    .55(20-x)+.80x = .70(20)

7.  Solve that and get x = 12.
8.  Answer: 12 quarts.

Edwin
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