SOLUTION: How many liters of 80% alcohol solution must be added to 20 liters of 90% alcohol solution to produce 85% alcohol solution?

Question 719586: How many liters of 80% alcohol solution must be added to 20 liters of 90% alcohol solution to produce 85% alcohol solution?
Found 2 solutions by mananth, jsmallt9:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
-------------- percent ---------------- Amount
Alcohol I 90 ---------------- 20 liters
Alcohol II 80 ---------------- x liters
Mixture 85 ---------------- 20 + x liters

90 * 20 + 80 x = 85 ( 20 + x )
1800 + 80 x = 1700 + 85 x
80 x -85 x = -1800 + 1700
-5 x = -100
/ -5
x = 20 liters Alcohol II

m.ananth@hotmail.ca

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Often the key to these mixture problems is to find expressions for the actual amount of the dissolved/mixed-in element in each of the mixtures/solutions. In this case, we are going to look to express the amount of alcohol.

When "A" is some percent of some solution/mixture, then the actual amount of A in the solution/mixture will be:
(percent as a decimal or fraction) * (the total amount of that mixture/solution)
(Note: Don't use a percent as a percent in an equation. Use the decimal or fraction equivalent instead.) Let's use this expression to express the amount of alcohol in the three solutions.

For the 80% solution, we do not know how much of it will be used. (In fact that is what we are trying to figure out.) Let's call this "x". So the amount of alcohol in this solution would be:
0.80 * x or just 0.80x
For the 90% solution we will be using 20 liters. So the alcohol in this solution will be:
0.90 * 20 or 18 liters
For the 85% solution, we do not know how much of that we will end up with either. But we do know that the amounts of the 80% and 90% solutions will add to the amount of 85% solution. So the amount of 85% solution will be x + 20. This makes the amount of alcohol in this solution:
0.85 * (x + 20) or 0.85x + 1.7

Now that we have the expressions we were looking for we are ready to solve the problem. Not only do the amounts of the 80% and 90% solutions add up the amount of 85% solution, but the amounts of alcohol in these solutions add up, too:
0.80x + 18 = 0.85x + 17
With this equation we can solve for x.

We can solve for x with the decimals in there. But I like to get rid of them. Multiplying by 100 will shift all the decimals over by two places:
80x + 1800 = 85x + 1700
Subtracting 80x:
1800 = 5x + 1700
Subtracting 1700:
100 = 5x
Dividing by 5:
20 = x
So we use 20 liters of the 80% solution.

P.S. You get the exact same answer if you leave the decimals in while solving.
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