SOLUTION: A chemist needs to mix 20 liters of 40% salt solution with some 70% solution to get a mixture that is 50% salt. How many liters of 70% solution should be used?

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Question 147292: A chemist needs to mix 20 liters of 40% salt solution with some 70% solution to get a mixture that is 50% salt. How many liters of 70% solution should be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(amount of salt you end up with) / (total amount of solution) = % salt
Let x = amount of 70% solution to be added
How much salt is in the 20 liters of 40% solution?
+.4+%2A20+=+8 liters
How much salt is in the 70% solution?
.7x
How much total solution do you end up with?
20+%2B+x
So, the equation to use is:
%288+%2B+.7x%29+%2F+%2820+%2B+x%29+=+.5
multiply both sides by 20+%2B+x
8+%2B+.7x+=+.5%2A%2820+%2B+x%29
8+%2B+.7x+=+10+%2B+.5x
.2x+=+2
x+=+10
The chemist needs to add 10 liters of the 70% solution
check answer:
%288+%2B+.7x%29+%2F+%2820+%2B+x%29+=+.5
%288+%2B+.7%2A10%29+%2F+%2820+%2B+10%29+=+.5
%288+%2B+7%29+%2F+30+=+.5
15%2F30+=+.5
15+=+.5%2A30
15+=+15
OK