SOLUTION: What amount of each mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of a mixture which is 45% alcohol? What equation or equations will express th

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Question 759061: What amount of each mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of a mixture which is 45% alcohol? What equation or equations will express this problem?
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
This extremely common two-part mixture problem can be handled with two equations: One is a rational equation using two unknown variables and another is a simple sum linear equation using the same two unknown variables.

ASSIGN VARIABLES TO ALL QUANTITIES
H = concentration, such as percent, of the high concentration material
L = concentration such as percent, of the low concentration material
T = the target concentration desired for the mixture
M = amount of mixture at the target concentration
u = amount of low concentration material to use (unknown)
v = amount of high concentration material to use (unknown)

ACCOUNT FOR PURE COMPONENT
is the amount of pure component
The concentration is then in the quantity of mixture, M,
is the resulting percent concentration for this example.

ACCOUNT FOR MATERIAL AMOUNTS
Simply

EQUATIONS TO FORM THE SYSTEM
and

Solve the system for u and v.
Substitute the given known values to find the resulting values for u and v.