Question 1154014

How many gallons of 20% alcohol solution and 45% alcohol solution must be mixed to get 10 gallons of 25% alcohol solution?
<pre>I STRONGLY believe that these types of problems, when possible, need to be solved using ONLY 1 variable.
For one, they're less confusing, and 2) much, much less time-consuming.

Let the amount of 20% alcohol to mix be T
Then amount of 45% alcohol to mix = 10 - T
We then get: .2T + .45(10 - T) = .25(10)
.2T + 4.5 - .45T = 2.5
.2T - .45T = 2.5 - 4.5
- .25T = - 2
T, or {{{highlight_green(matrix(2,11, Amount, of, "20%", solution, to, mix, "=", (- 2)/(- .25), "=", 8, gallons, Amount, of, "45%", solution, to, mix, "=", 10 - 8, "=", 2, gallons))}}}