SOLUTION: How many gallons of 51% alcohol solution should be added to some of a 57% alcohol solution to make a 438 gal of a 55% solution? Thank you.

Question 30787: How many gallons of 51% alcohol solution should be added to some of a 57% alcohol solution to make a 438 gal of a 55% solution? Thank you.
Found 2 solutions by checkley71, Fermat:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
(.51X)+(438-X).57=(438).55
.51X+249.66-.57X=240.9
-.06X=-8.76 OR X=8.76/.06 OR 146 GAL OF .51 % & 438-146=292 GAL OF 57%

Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
Let there be X gall of 51% alcohol
Let there be Y gall of 57% alcohol
If a solution of alcohol, X gall, has 51% concentration, then 51% of that volume is pure alcohol and the remainder, 49%, is pure water.
51% alcohol: 0.51*X gall of pure alcohol and 0.49*X gall of pure water
57% alcohol: 0.57*Y gall of pure alcohol and 0.43*Y gall of pure water
adding the two mixtures together,
55% alcohol: (0.51*X + 0.57*Y) gall of pure alcohol and (0.49*X + 0.43*Y) gall of pure water.
Concentration of mixture = quantity of alcohol over quantity of mixture (water plus alcohol)
55% = (0.51X + 0.57Y) gall over (X + Y) galls
0.55 = (0.51X + 0.57Y)/(X + Y)
0.55(X+Y) = 0.51X + 0.57Y
substituting for X+Y = 438,
0.55*438 = 0.51X + 0.57Y
240.9 = 0.51X + 0.57Y
substituting for X = 438 - Y
240.9 = 0.51(438 - Y) + 0.57Y
240.9 = 223.38 - 0.51Y + 0.57Y
240.9 - 223.38 = -0.51Y + 0.57Y
17.52 = 0.06Y
Y = 17.52/0.06
Y = 192 gall
============
X = 146 gall
============
Ans: need 146 gall of 51% alcohol
==================================
RELATED QUESTIONS
How many gallons of pure alcohol solution should be added to 63 gal of 32% alcohol... (answered by checkley71,venugopalramana)
How many gallons of 16% alcohol solution should be added to 30 gal of a 45% alcohol... (answered by Paul,venugopalramana)
You have 18 milliliters of a 45% alcohol solution. How many milliliters of a 51% alcohol... (answered by stanbon)
How much alcohol must be added to 16 liters of a 25% alcohol solution to make a 55%... (answered by stanbon)
How many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to (answered by wgunther)
how many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to (answered by nyc_function)
How many gallons of pure alcohol should be mixed with 20 gal of 15% alcohol solution to... (answered by jorel1380)
Alcohol Mixture. How may gallons of pure alcohol should be mixed with 20 gal of a 15%... (answered by josgarithmetic)
how many gallons of pure alcohol must be added to 5 gallons of 20% alcohol solustion to... (answered by edjones)