Solution Y is 40 percent sugar by volume, and solution X is 20 percent

In order to solve this problem you must be able to translate English into Algebra equations. Once you have written one or more algebraic equations it becomes a simple math problem to solve. You should look out for some keywords such as added, percent and so on while creating the equations. In this case, lets go step by step:

1. The problem states that there is 150 gallons of Y solution and X will be added to create a solution - this shows that the total number of gallons in the new solution will be \(150+x\).
2. The new solution is 25 percent sugar by volume. So, that becomes \(\frac{25}{100}* (150+x)\).
3. Solution Y is 40 percent sugar and we know that there are 150 gallons of Y solution. Solving for that gives \(\frac{40}{100} * 150\). This gives us 60 gallons of sugar by volume in Solution Y out of the 150 total gallons
4. Solution X is 20 percent sugar and this will be added to 60 gallons of Y. So the translation here is \(60 + \frac{20}{100}(x)\)

Now we can form the equation -> \(60 + \frac{20}{100}(x) = \frac{25}{100}(150+x)\)

This is solving equation with one variable.

\(60 + 0.2x = 37.5 + .25x\)

\(.05x = 22.5\)

\(x = 450\)

The answer is E.