Tank A contains a mixture of 10 gallons water and 5 gallons pure alcohol. Tank B has 12 gallons water and 3 gallons alcohol. How many gallons should be taken from each tank and combined in order to obtain an 8 gallon solution containing 25% alcohol by volume?
we know that The mixture in Tank A is 5/(5+10) = 1/3 pure alcohol. The mixture in Tank B is 3/(3+12) = 1/5 pure alcohol. We want to combine these to make a mixture that is 25% = 1/4 pure alcohol. Let x------------------> the volume in gallons of solution taken from Tank A. y------------------>the volume in gallons of solution taken from Tank B Then the volume taken from Tank B will be y=(8 -x) remember that we are making a total of 8 gallons of solutions.
The alcohol content of the mixture is(1/3)x +(1/5)(8 -x) = (1/4)*85x + 3(8 -x) = 30 ----------> 5x+24-3x=30----------> 5x-3x=30-24 2x = 6 ----------------> x=3 y=8-x--------> y=8-3-----> y=5
the answer is 3 gallons should be taken from Tank A; 5 gallons should be taken from Tank B
