SOLUTION: A car radiator has a 6-liter capacity. If the liquid in the radiators 40% antifreeze, how much liquid must be replaced with pure antifreeze to bring the mixture up to a 50% solutio

Algebra ->  Conversion and Units of Measurement -> SOLUTION: A car radiator has a 6-liter capacity. If the liquid in the radiators 40% antifreeze, how much liquid must be replaced with pure antifreeze to bring the mixture up to a 50% solutio      Log On


   

Question 312145: A car radiator has a 6-liter capacity. If the liquid in the radiators 40% antifreeze, how much liquid must be replaced with pure antifreeze to bring the mixture up to a 50% solutions?
Found 2 solutions by redheadtie, Fombitz:
Answer by redheadtie(3) About Me  (Show Source):
You can put this solution on YOUR website!
2.5 more liters

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 40% solution currently in the radiator. You add B liters of pure antifreeze (100% solution).
1.40%28A%29%2B100%28B%29=50%28A%2BB%29
2.A%2BB=6
From eq. 2,
A=6-B
Substitute into eq. 1,
40%286-B%29%2B100%28B%29=50%286-B%2BB%29
240-40B%2B100B=300
60B=60
highlight%28B=1%29
Then from eq. 2,
A=6-B=6-1
highlight%28A=5%29
There are currently 5 liters of 40% solution. Adding 1 liter will fill the radiator and make a 50% solution.