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