SOLUTION: suppose that you have a supply of a 20% solution of alcohol and a 70% solution of alcohol. How man quarts of each should be mixed to produce 50 quarts that is 40% alcohol?

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Question 784974: suppose that you have a supply of a 20% solution of alcohol and a 70% solution of alcohol. How man quarts of each should be mixed to produce 50 quarts that is 40% alcohol?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ASSIGN VARIABLES
H = 70%
L = 20%
T = 40%, concentration wanted
M = 50 quarts, quantity wanted
u = unknown volume of 20%
v = unknown volume of 70%


MAKE EQUATIONS FOR SYSTEM

highlight%28%28Lu%2BHv%29%2FM=T%29 and highlight%28u%2Bv=M%29

Solve for u and v. The equations will be linear so the rational one with T is easily transformed into a more familiar format.

v=M-u, and Lu%2BHv=TM%2C
Lu%2BH%28M-u%29=TM
Lu-Hu%2BHM=TM
%28L-H%29u=TM-HM
u=%28TM-HM%29%2F%28L-H%29
u=M%28T-H%29%2F%28L-H%29
Divide by or multiply by %28-1%29%2F%28-1%29 because computations will be easier that way:
highlight%28u=M%28H-T%29%2F%28H-L%29%29
'
Use that for u and then go back to highlight%28v=M-u%29.

SUBSTITUTE THE GIVEN VALUES TO FIND THE UNKNOWN VALUES
Just use the number values from the description, listed as "ASSIGN VARIABLES".