SOLUTION: If you have supplies of 2% alcohol and 6% alcohol. How much of each would you mix to obtain 60 liters of 3.2$ alcohol?

Question 166423: If you have supplies of 2% alcohol and 6% alcohol. How much of each would you mix to obtain 60 liters of 3.2$ alcohol?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = amount of 2% alcohol solution.
let y = amount of 6% alcohol solution.
let z = amount of 3.2% alcohol solution.
z = 60 liters.
-----
x amount of 2% alcohol solution + y amount of 6% alcohol solution = 60 liters of 3.2% alcohol solution.
x + y = z
z = 60
equation for that is:
x + y = 60 (equation 1)**********************************
-----
.02 * x = amount of alcohol in 2% solution.
.06 * y = amount of alcohol in 6% solution.
.032 * z = amount of alcohol in 3.2% solution.
z = 60
.032 * 60 = 1.92 liters of alcohol in 60 liters of 3.2% solution.
the amount of alcohol in the 2% solution plus the amount of alcohol in the 6% solution must total up to be 1.96 liters of alcohol.
equation for that is:
.02*x + .06*y = 1.96 (equation 2)***********************************
-----
two equations to solve are:
x + y = 60 (equation 1)
.02*x + .06*y = 1.92 (equation 2)
-----
multiply equation 2 by 50:
x + y = 60 (equation 1)
x + 3*y = 96 (equation 2)
subtract equation 1 from equation 2:
2*y = 36
y = 18
-----
if y = 18, then x must = 42 since x + y = 60 (equation 1)
-----
answer is:
42 liters of 2% solution plus 18 liters of 6% solution equals 60 liters of 3.2% solution.
-----
x = 42
y = 18
x + y = 60 (equation 1)
42 + 18 = 60
60 = 60
equation 1 is good
-----
.02*x + .06*y = .032*z (equation 2)
.02*42 + .06*18 = .032*60
.84 + 1.08 = 1.92
1.92 = 1.92
-----
both equations are satisfied so answer is good.

RELATED QUESTIONS
Could you please help me with this problem. I am supposed to use a system of equations to (answered by ankor@dixie-net.com)

You have a solution that is 50% alcohol and a solution that is 80% alcohol. How much of... (answered by nerdybill)

Solution x is 2% alcohol and solution y is 6% alcohol. A drugstore owner wants to mix... (answered by longjonsilver)

You wish to mix wine with 25% alcohol and peach schnapps with 50% alcohol to obtain a... (answered by funmath)

solution A is 2% alcohol. solution B is 6% alcohol A service station owner wants to mix... (answered by stanbon)

solution A is 2% alcohol. Solution B is 6% alcohol. A service station owner wants to mix... (answered by stanbon)

If you need to mix 5L of fluid containing 25%alcohol and you have one that cotains... (answered by stanbon)

How many liters of 70% alcohol and 40% solution must be mixed to obtain 6 liters of 60%... (answered by josgarithmetic,addingup)

One alcohol solution contains 10% alcohol and another contains 25% alcohol. How much of... (answered by josgarithmetic)