SOLUTION: a scientist needs 30 liters of a 60% solution. He has a 40% solution and a 70% solution. How many of each does he need to get 30 liters of a 60% solution?

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Question 712266: a scientist needs 30 liters of a 60% solution. He has a 40% solution and a 70% solution. How many of each does he need to get 30 liters of a 60% 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 40%
H, the higher concentration of available material 70%
T, the target concentration of resulting mixture 60%
x, the amount of lower concentrated material to use, unknown
y, the amount of higher concentrated materaial to use, unknown
M, amount of the resulting mixture 30 Liters


EQUATIONS
highlight%28%28Lx%2ByH%29%2FM=T%29
highlight%28x%2By=M%29

SOLVE SYMBOLICALLY
%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 you substitute the values and compute x, use y=M-x to compute the value for y.

highlight%28x=%2830%2870-60%29%29%2F%2870-40%29%29, ... and you know what else to do..