ALgebra problem!?

Question

Suppose that you have a supply of a 15% solution of alcohol and a 45%
solution of alcohol. How many quart of each should be mixed to produce 30
quarts that is 25% alcohol?

Answer 1

Let's say that you add x quarts of 15%, to (30-x) quarts of 45%. The amount of alcohol you'll have is then:

0.15x + 0.45(30-x)

If you want to have 25% solution, that should also equal the amount of alcohol in 30 quarts of a 25% solution (0.25*30).

That's the equation to solve:

0.15x + 0.45(30 - x) = 0.25*30
13.5 - 0.30x = 7.5
0.30x = 6
x = 6/0.30
x = 20

20 quarts of 15%
10 quarts of 45%

Checking the answer:

20*0.15 + 10*0.45 =
3 + 4.5 =
7.5 quarts of alcohol

7.5/30 = 0.25, which is 25%

Answer 2

Let x qt be the amount of the 15% alcohol solution,
then (30-x) qt is the amount of the 45% solution
Amount of alcohol from the mixed solution
= .15x + .45(30-x)
we want this to be 25% of 30 qt = 30 x .25 = 7.5

0.15x + 0.45(30-x) = 7.5
-0.3x + 13.5 = 7.5
0.3x = 13.5 - 7.5 = 6
x = 6/0.3 = 20

Ans: Use 20 qt of 15% alcohol solution,
and 10 qt of 45% alcohol solution,
and you will get 30qt of 25% alcohol solution,