SOLUTION: I keep having issues trying to figure out this problem. Anyone help? A 75% alcohol solution is to be mixed with 50% alcohol solution to obtain 12 liters of a 60% alcohol solutio

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Question 870078: I keep having issues trying to figure out this problem. Anyone help?
A 75% alcohol solution is to be mixed with 50% alcohol solution to obtain 12 liters of a 60% alcohol solution? How many liters of the acid 75% solution should be used?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x is the number of liters of 75% solution.
y is the number of liters of 50% solution.

you have 2 equations to work with.

The first equation is:
x + y = 12
The second equation is:
.75*x + .5*y = .6*(x+y)

Since x + y = 12, the second equation becomes:
.75*x + .5*y = .6*12 which becomes:
.75*x + .5*y = 7.2

Use the first equation to solve for y to get:
y = 12 - x

Replace y with 12 - x in the second equation to get:
.75*x + .5*(12-x) = 7.2
Simplify to get:
.75*x + .5*12 - .5*x = 7.2
Simplify by combining like terms and performing the indicated operations to get:
.25*x + 6 = 7.2
subtract 6 from both sides of this equation to get:
.25*x = 1.2
divide both sides of this equation by .25 to get:
x = 1.2 / .25 = 4.8

you have x = 4.8
since x+y = 12, then y must be equal to 7.2

you have x + y = 12 which becomes 4.8 + 7.2 = 12 which becomes 12 = 12.
this confirms the first equation is good when x = 4.8 and y = 7.2

you have .75*x + .5*y = .6*12 which becomes .75*4.8 + .5*7.2 = 7.2 which becomes 3.6 + 3.6 = 7.2 which becomes 7.2 = 7.2.
this confirms the second equation is good when x = 4.8 and y = 7.2.