SOLUTION: What quantity of a 55% acid solution must be mixed with a 45% solution to produce 600 mL of a 50% solution?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: What quantity of a 55% acid solution must be mixed with a 45% solution to produce 600 mL of a 50% solution?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 784649: What quantity of a 55% acid solution must be mixed with a 45% solution to produce 600 mL of a 50% solution?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ASSIGN VARIABLES TO ALL QUANTITIES
L, the lower concentration of available material, 45%
H, the higher concentration of available material, 55%
T, the target concentration of resulting mixture, 50%
M, the amount of resulting mixture, 600 ml.
x, the amount of lower concentrated material to use, unknown
y, the amount of higher concentrated material to use, unknown

EQUATION
highlight%28%28Lx%2ByH%29%2FM=T%29 and highlight%28x%2By=M%29
%28Lx%2ByH%29%2FM=T
Lx%2ByH=TM
Lx%2B%28M-x%29H=TM
Lx%2BHM-Hx=TM
%28L-H%29x%2BHM=TM
%28L-H%29x=TM-HM
%28L-H%29x=%28T-H%29M
x=M%28T-H%29%2F%28L-H%29, and since the two differences here would both be negative,
we can multiply by (-1)/(-1),
highlight%28x=M%28H-T%29%2F%28H-L%29%29

After using that formula, you can simply use highlight%28y=M-x%29

Substitute the necessary values and compute x and y.