SOLUTION: how many liters of water should be added to 20 liters of a 70 percent antifreeze solution to make a 50 percent antifreeze solution?

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Question 913873: how many liters of water should be added to 20 liters of a 70 percent antifreeze solution to make a 50 percent antifreeze solution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
how many liters of water should be added to 20 liters of a 70 percent antifreeze solution to make a 50 percent acid solution?
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"20 liters of a 70 percent antifreeze solution" means we have

20*0.70 = 14 liters of pure antifreeze
20-14 = 6 liters of pure water (alternate calculation: 20*0.3 = 6)

Let x = amount of pure water to add

We have 14 liters of pure antifreeze. This figure does NOT change when we add the pure water.

We have 20 liters of solution. This gets bumped up to 20+x when we add the pure water.

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So we go from 14%2F20 to 14%2F%2820%2Bx%29. The fraction represents the percentage of antifreeze in the solution.

We want this percentage to be 50%, so set the fraction equal to 0.50 and solve for x. 

	14%2F%2820%2Bx%29=0.50
	
	
	14=0.50%2820%2Bx%29
	
	
	14=0.50%2820%29%2B0.50%28x%29
	
	
	14=10%2B0.50x
	
	
	14-10=0.50x
	
	
	4=0.50x
	
	
	4%2F0.50=x
	
	
	8=x
	
	
	x=8


So you need to add 8 liters of pure water to make a 50 percent antifreeze solution.

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim