# How many gallons of 20% alcohol solution and 45% alcohol solution must be mixed to get 20 gallons of 25% alcohol solution?

##### 1 Answer

20 gallons of 25% alcohol can be constructed with 16 gallons of 20% alcohol mixed with 4 gallons of 45% alcohol.

#### Explanation:

Note that the amount of alcohol in a solution is

amount of alcohol = number of gallons

For example, in the final mixture, we want 20 gallons of 25% alcohol. The amount of alcohol in this amount of solution will be

final amount of alcohol =

Let

This means that the number of gallons of 45% solution is

Because this is a mixture problem and there is no chemical reaction taking place (no alcohol is created or destroyed in the mixture process) we must start with 5 gallons alcohol. This means that the amount of alcohol in the 20% solution plus the amount of alcohol in the 45% solution must add up to 5 gallons. We can express this mathematically as

I prefer to work with fractions so I will rewrite this equation as

Apply the distributive property.

Subtract 9 from both sides of this equation.

Multiply both sides of this equation by

Multiply both sides of this equation by 20.

Combine like terms.

Divide both sides by 5.

This means that we need