For problem #1, you know you need to end up with 50 liters of 25% alcohol. In other words, you need to end up with 12.5 liters of total, pure alcohol (50 * .25).

Let's say you use x liters of the 33 1/3% alcohol. This gives you x/3 liters of pure alcohol.

Then, since you need 50 total liters, you must use 50 - x liters of the 12.5% alcohol mixture. This gives you (50 - x)*.125 = 6.25 - .125x liters of pure alcohol.

Combine the two amounts you get from the mixtures and set it equal to the final total.

In other words, x/3 + 6.25 - .125x = 12.5. Now, solve for x - first, I'd multiply everything by 3 to get rid of the fraction:

x + 18.75 - .375x = 37.5

Move the 18.75 to the other side and combine the two x terms on the left:

.625x = 18.75.

Divide by .625:

x = 30.

Remember what you chose x to represent: the 33 1/3% alcohol mixture. So you need 30 liters of that and 20 of the other.