Hey,
I could really use some help solving this mixtures problem. Normally I can just work it out but this one is a little bit different than most.
A solution of 90% alcohol is mixed with a solution of 30% alcohol that is smaller by 20 liters. After 15 liters of water evaporates from the solution, the alcohol content is 72%. How many liters of solution is in the final mixture.
Could really use help working out the method used to solve this type of problem
EDIT:
Solution 1: 90% Alcohol, Volume x
Solution 2: 30% Alcohol, Volume x-20
Total Solution: 72% Alcohol, Volume x+x-20-15 OR 2x-35
This is all the information given. I need to determine that volume in liters of the total solution.
That is exactly the problem, the only given is that it is 20 liters smaller than the first solution. It contains 30% alcohol
Edit: Basically my givens are
Solution 1: 90% alcohol, volume x
Solution 2: 30% alcohol, volume x-20
Final Solution: 72% alcohol, volume x+x-20-15 (2x-35)
x + x - 20, - 15 or 2x-35
However, that does not give me a number of liters in the final solution.
Working it out through trial and error is simple if tedious. I just need to find a way to do it algebraically so when faced with similar questions I don't have to waste all that time
Edit: If you are asking however, how many liters are given for each solution, then that is exactly the question I am supposed to solve. None are given
Hello, asdewq!
This is a tricky one . . .
We will consider the amount of water at each stage.A solution of 90% alcohol is mixed with a solution of 30% alcohol that is smaller by 20 liters.
After 15 liters of water evaporates from the solution, the alcohol content is 72%.
How many liters of solution is in the final mixture?
Let = liters of the 90% alcohol solution.
This contains liters of water.
Let = liters of the 30% alcohol solution.
This contains liters of water.
Then 15 liters of water is removed.
The mixture contains: liters of water. .[1]
The final mixture contains: liters .(a)
. . which is 28% water.
The mixture contains: liters of water. .[2]
We just described the final amount of water in two ways.
There is our equation! . . . .
Solve for
Substitute into (a): . liters.