SOLUTION: Chemist has 10% solution and 60%solution; how many liters of each solution does the chemist need to make 200 liters of a solution that is 50%acid?

Question 804046: Chemist has 10% solution and 60%solution; how many liters of each solution does the chemist need to make 200 liters of a solution that is 50%acid?
Found 2 solutions by richwmiller, AlgebraLady88:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
.1x+.6y=.5*200,
x+y=200
x=40., y=160.
Answer by AlgebraLady88(44) (Show Source): You can put this solution on YOUR website!
In this question, we can see that we have two types of solutions here: the 10 % solution and the 60% solution and that altogether, we need 200 liters of a solution that is 50 % acid.

x stands for the 10 % solution and y stands for the 60 % solution. We need 200 liters of the solution. Hence:
x + y = 200 (a)
The next equation would be what is needed to make 200 liters that is 50% acid.
Hence:
0.10x+0.60y = 0.50 * 200
0.10x+0.60y = 100
Multiply by 10 to get rid of decimals: x+ 6y = 1000 (b)
Multiply (a) by -1 and then we can add equations (a) and (b)
-x-y = -200 (a)
x+6y = 1000 (b)
5y = 800
y = 160
This will give us x+y = 200
x = 200- 160
x = 40

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