SOLUTION: Hi, I am stuck on this one. Nothing I have tried makes sense. Help would be very appreciated. How many ml of medication A which has a 20% concentration, and medication B which

Question 310567: Hi, I am stuck on this one. Nothing I have tried makes sense. Help would be very appreciated.
How many ml of medication A which has a 20% concentration, and medication B which has a 65% concentration should be mixed to form a 550 ml solution that is 30.9%

This is what I came up with .2x + .35(550-x) = .309
If you can just explain how to set up the equation and the answer to check my work from I can solve it.
Thanks
April

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many ml of medication A which has a 20% concentration, and medication B which has a 65% concentration should be mixed to form a 550 ml solution that is 30.9%
-------------------------------
Equation:
Quantity Equation:::::::: a + b = 550 ml
Active Ingredient Eq: 0.20a + 0.65b = 0.309*550
----------------------
Solving using 2 equations and elimination:
Multiply thru the 1st equation by 20
Multiply thru the 2nd equation by 100
----------------------------------------
20a + 20b = 20*550
20a + 65b = 30.9*550
----------------------------
Subtract 1st from 2nd and solve for "b":
45b = 10.9*550
b = 133.22 ml (amt. of 65% solution needed in the mixture)
----
Since a + b = 550, a = 416.78 ml (amt. of 20% solution needed in the mix)
=============================================================================
cheers,
Stan H.
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