SOLUTION: if a nurse needs two liter of a 4% solution of a certain medication, and she only has a 2% solution and a 10% solution to work with, how much of each should she mix together to get

Question 661140: if a nurse needs two liter of a 4% solution of a certain medication, and she only has a 2% solution and a 10% solution to work with, how much of each should she mix together to get what she needs?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = 2% solution
y = 10% solution
you need to put together 2 liters of a 4% solution
x + y = 2
.02x + .10y = 2*.04
simplify to get:
.02x + .10y = .08
solve for y in the first equation to get y = 2 - x
substitute 2 - x for y in the second equation to get .02x + .10 * (2-x) = .08
simplify to get .02x + .20 - .10x = .08
combine like terms to get -.08x + .20 = .08
subtract .20 from both sides of the equation to get -.08x = -.12
divide both sides of the equation by -.08 to get x = 1.5
since x + y = 2, then y = .5 and you have:
x = 1.5
y = .5
substitute in the first equation to get x + y = 2 becomes 1.5 + .5 = 2 which becomes 2 = 2 which is true.
substitute in the second equation to get .02x + .10y = .08 becomes .02*1.5 + .10*.5 = .08 which becomes .03 + .05 = .08 which becomes .08 = .08 which is true.
since both original equations are true, then x = 1.5 and y = .5 is a solution to both equations and you're good.

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